R s aggarwal solutions mathematics class 9 Solutions for Chapter 15 volume and surface area of solids

Find the volume, the lateral surface area, and the total surface area of the cuboid whose dimensions are:

length = 12cm, breadth = 8cm and height = 4.5cm

Find the volume, the lateral surface area, and the total surface area of the cuboid whose dimensions are:

length = 26m, breadth = 14m and height = 6.5m

Find the volume, the lateral surface area, and the total surface area of the cuboid whose dimensions are:

length = 15m, breadth = 6m and height = 5dm

Find the volume, the lateral surface area, and the total surface area of the cuboid whose dimensions are:

length = 24m, breadth = 25cm and height = 6m.

A matchbox measure 4cm × 2.5cm × 1.5 cm. What is the volume of a packet containing 12 such matchboxes?

A cuboidal water tank is 6m long, 5m wide, and 4.5m deep. How many liters of water can it hold? (Given,1m3 = 1000 litres.)

The capacity of a cuboidal tank is 50000 litres of water. Find the breadth of the tank if its length and depth are respectively 10m and 2.5m. (Given, 1000 litres = 1m3.)

A godown measure 40m × 25m × 15m. Find the maximum number of wooden crates, each measuring 1.5m × 1.25m × 0.5m that can be stored in the godown.

How many planks of dimensions (5m × 25cm × 10cm) can be stored in a pit which is 20m long, 6m wide and 80cm deep?

How many bricks will be required to construct a wall 8m long, 6m high, and 22.5cm thick if each brick measures (25cm × 11.25cm × 6cm)?

Find the capacity of a closed rectangular cistern whose length is 8m, breadth 6m and depth 2.5m. Also, find the area of the iron sheet required to make the cistern.

The dimensions of a room are (9m × 8m × 6.5m). It has one door of dimensions (2m × 1.5m) and two windows, each of dimensions (1.5m × 1m). Find the cost of whitewashing the walls at ₹ 25 per square metre.

A wall 15m long, 30cm wide and 4m high is made of bricks, each measuring (22cm × 12.5cm × 7.5cm). If 1/12 of the total volume of the wall consists of mortar, how many bricks are there in the wall?

How many cubic centimeters of iron are there in an open box whose external dimensions are 36cm, 25cm, and 16.5cm, the iron being 1.5cm thick throughout? If 1cm3 of iron weighs 15g, find the weight of the empty box in kilograms.

A box made of sheet metal costs ₹ 6480 at ₹ 120 per square meter. If the box is 5m long and 3m wide, find its height.

The volume of a cuboid is 1536m3. Its length is 16m, and its breadth and height are in the ratio 3:2. Find the breadth and height of the cuboid.

How many persons can be accommodated in a dining hall of dimensions (20m × 16m × 4.5m), assuming that each person requires 5 cubic meters of air?

A classroom is 10m long, 6.4m wide and 5m high. If each student be given 1.6m2 of the floor area, how many students can be accommodated in the room? How many cubic metres of air would each student get?

The surface area of a cuboid is 758cm2. Its length and breadth are 14cm and 11cm respectively. Find its height.

In a shower, 5cm of rain falls. Find the volume of water that falls on 2 hectares of ground.

Find the volume, the lateral surface area, the total surface area and the diagonal of a cube, each of whose edges measures 9m. (Take √3 = 1.73)

The total surface area of a cube is 1176 cm2. Find its volume.

The lateral surface area of a cube is 900 cm2. Find its volume.

The volume of a cube is 512cm3. Find its surface area.

Three cubes of metal with edges 3cm, 4cm and 5cm respectively are melted to form a single cube. Find the lateral surface area of the new cube formed.

Find the length of the longest pole that can be put in a room of dimensions (10m × 10m × 5m).

The sum of length, breadth and depth of a cuboid is 19cm and the length of its diagonal is 11cm. Find the surface area of the cuboid.

Each edge of a cube is increased by 50%. Find the percentage increase in the surface area of the cube.

If V is the volume of a cuboid of dimensions a, b, c and S is its surface area then prove that 1/V = 2/S (1/a + 1/b + 1/c).

Water in a canal, 30dm wide and 12dm deep, is flowing with a velocity of 20km per hour. How much area will it irrigate, if 9cm of standing water is desired?

A solid metallic cuboid of dimensions (9m × 8m × 2m) is melted and recast into solid cubes of edge 2m. Find the number of cubes so formed.

The diameter of a cylinder is 28cm and its height is 40cm. Find the curved surface area, total surface area and the volume of the cylinder.

A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7cm. If the bowl is filled with soup to a height of 4cm, how much soup the hospital has to prepare daily to serve 250 patients?

The pillars of a temple are cylindrically shaped. Each pillar has a circular base of radius 20cm and height 10m. How much concrete mixture would be required to build 14 such pillars?

A soft drink is available in two packs:

A tin can with a rectangular base of length 5cm, breadth 4cm and height 15cm,

Which container has greater capacity and by how much?

A soft drink is available in two packs:

A plastic cylinder with circular base of diameter 7cm and height 10cm.

Which container has greater capacity and by how much?

There are 20 cylindrical pillars in a building, each having a diameter of 50cm and height 4m. Find the cost of cleaning them at ₹ 14 per m2.

The curved surface area of a right circular cylinder is 4.4 m2. If the radius of its base is 0.7m, find its volume.

The curved surface area of a right circular cylinder is 4.4 m2. If the radius of its base is 0.7m, find its height.

The lateral surface area of a cylinder is 94.2 cm2 and its height is 5cm. Find its volume. (Take π = 3.14)

The lateral surface area of a cylinder is 94.2 cm2 and its height is 5cm. Find the radius of its base.

The capacity of a closed cylindrical vessel of height 1m is 15.4 litres. Find the area of the metal sheet needed to make it.

The inner diameter of a cylindrical wooden pipe is 24cm and its outer diameter is 28cm. The length of the pipe is 35cm. Find the mass of the pipe, if 1cm3 of wood has a mass of 0.6g.

In a water heating system, there is a cylindrical pipe of length 28m and diameter 5cm. Find the total radiating surface in the system.

Find the weight of a solid cylinder of radius 10.5cm and height 60cm if the material of the cylinder weighs 5g per cm3.

The curved surface area of a cylinder is 1210 cm2 and its diameter is 20cm. Find its height and volume.

The curved surface area of a cylinder is 4400 cm2 and the circumference of its base is 110cm. Find the height and the volume of the cylinder.

The radius of the base and the height of a cylinder are in the ratio 2: 3. If its volume is 1617cm3, find the total surface area of the cylinder.

The total surface area of a cylinder is 462cm2. Its curved surface area is one-third of its total surface area. Find the volume of the cylinder.

The total surface area of a solid cylinder is 231 cm2 and its curved surface area is 2/3 of the total surface area. Find the volume of the cylinder.

The ratio between the curved surface area and the total surface area of a right circular cylinder is 1: 2.

Find the volume of the cylinder if its total surface area is 616 cm2.

A cylindrical bucket, 28cm in diameter and 72cm high, is full of water. The water is emptied into a rectangular tank, 66cm long and 28cm wide. Find the height of the water level in the tank.

The barrel of a fountain pen, cylindrical in shape, is 7cm long and 5mm in diameter. A full barrel of ink in the pen will be used up on writing 330 words on an average. How many words would use up a bottle of ink containing one fifth of a litre?

1cm3 of gold is drawn into a wire 0.1mm in diameter. Find the length of the wire.

If 1cm3 of cast iron weighs 21g, find the weight of a cast iron pipe of length 1m with a bore of 3cm in which the thickness of the metal is 1cm.

A cylindrical tube, open at both ends, is made of metal. The internal diameter of the tube is 10.4cm and its length is 25cm. The thickness of the metal is 8mm everywhere. Calculate the volume of the metal.

It is required to make a closed cylindrical tank of height 1m and base diameter 140cm from a metal sheet. How many square metres of the sheet are required for the same?

A juice seller has a large cylindrical vessel of base radius 15cm filled up to a height of 32cm with orange juice. The juice is filled in small cylindrical glasses of radius 3cm up to a height of 8cm, and sold for ₹ 15 each. How much money does he receive by selling the juice completely?

A well with inside diameter 10m is dug 8.4m deep. Earth taken out of it is spread all around it to a width of 7.5m to form an embankment. Find the height of the embankment.

How many liters of water flow out of a pipe having an area of cross-section of 5cm2 in 1 minute, if the speed of water in the pipe is 30cm/sec?

A cylindrical water tank of diameter 1.4m and height 2.1m is being fed by a pipe of diameter 3.5cm through which water flows at the rate of 2m per second. In how much time will the tank be filled?

A cylindrical container with a diameter of base 56cm contains sufficient water to submerge a rectangular solid of iron with dimensions (32cm × 22cm × 14cm). Find a rise in the level of water when the solid is completely submerged.

Find out the cost of sinking a tube-well 280m deep, having a diameter of 3m at a rate of ₹ 15 per cubic meter. Also, find the cost of cementing its inner curved surface at ₹ 10 per square meter.

Find a length of 13.2 kg of copper wire of diameter 4mm, when 1 cubic centimeter of copper weighs 8.4kg.

It costs ₹ 3300 to paint the inner curved surface of a cylindrical vessel 10m deep at the rate of ₹ 30 per m2.

Find the inner curved surface area of the vessel,

It costs ₹ 3300 to paint the inner curved surface of a cylindrical vessel 10m deep at the rate of ₹ 30 per m2.

Find the inner radius of the base,

It costs ₹ 3300 to paint the inner curved surface of a cylindrical vessel 10m deep at the rate of ₹ 30 per m2.

Find the capacity of the vessel.

The difference between the inside and outside surfaces of a cylindrical tube 14cm long is 88cm2. If the volume of the tube is 176 cm3, find the inner and outer radii of the tube.

A rectangular sheet of paper 30cm × 18cm can be transformed into the curved surface of a right circular cylinder in two ways namely, either by rolling the paper along its length or by rolling it along with its breadth.

Find the ratio of the volumes of the two cylinders, thus formed.

Find the curved surface area of the cone with a base radius of 5.25cm and a slant height 10cm.

Find the total surface area of a cone, if its slant height is 21m and the diameter of its base is 24m.

A joker’s cap is in the form of a right circular cone of base radius 7cm and height 24cm. Find the area of the sheet required to make 10 such caps.

The curved surface area of a cone is 308cm2 and its slant height is 14cm. Find the radius of the base and total surface area of the cone.

The slant height and a base diameter of a conical tomb are 25m and 14m, respectively. Find the cost of whitewashing its curved surface at the rate of ₹ 12 per m2.

A conical tent is 10m high and the radius of its base is 24m. Find the slant height of the tent. If the cost of 1m2 canvas is ₹ 70, find the cost of canvas required to make the tent.

A bus stop is barricaded from the remaining part of the road by using 50 hollow cones made of recycled cardboard. Each one has a base diameter of 40cm and height 1m. If the outer side of each of the cones is to be painted and the cost of painting is ₹ 25 per m2, what will be the cost of painting all these cones? (Use π = 3.14 and √1.04 = 1.02.)

Find the volume, curved surface area, and the total surface area of a cone having a base radius 35cm and height 12cm.

Find the volume, curved surface area and the total surface area of a cone whose height is 6cm and slant height 100cm. (Take π = 3.14.)

A conical pit of diameter 3.5m is 12m deep. What is its capacity in kilolitres?

A heap of wheat is in the form of a cone of diameter 9m and height 3.5m. Find its volume. How much canvas cloth is required to just cover the heap? (Use π = 3.14.)

A man uses a piece of canvas having an area of 551m2, to make a conical tent of base radius 7m. Assuming that all the stitching margins and wastage incurred while cutting, amount to approximately 1m2, find the volume of the tent that can be made with it.

How many meters of cloth, 2.5m wide, will be required to make a conical tent whose base radius is 7m and height 24m?

Two cones have their heights in the ratio 1:3 and the radii of their bases in the ratio 3:1. Show that their volumes are in the ratio 3:1.

A cylinder and a cone have equal radii of their bases and equal heights. If their curved surface areas are in the ratio 8:5, show that the radius and height of each has the ratio 3:4.

A right circular cone is 3.6cm high and radius of its base is 1.6cm. It is melted and recast into a right circular cone having base radius 1.2cm. Find its height.

A circus tent is cylindrical to a height of 3 metres and conical above it. If its diameter is 15m and the slant height of the conical portion is 53m, calculate the length of the canvas 5m wide to make the required tent.

An iron pillar consists of a cylindrical portion 2.8m high and 20cm in diameter and a cone 42cm high is surmounting it. Find the weight of the pillar, given that 1cm3 of iron weighs 7.5g.

From a solid right circular cylinder with height 10cm and radius of the base 6cm, a right circular cone of the same height and base is removed. Find the volume of the remaining solid. (Take π = 3.14.)

Water flows at the rate of 10 metres per minute through a cylindrical pipe 5mm in diameter. How long would it take to fill a conical vessel whose diameter at the surface is 40cm and depth 24cm?

A cloth having an area of 165 m2 is shaped into the form of a conical tent of radius 5m.

How many students can sit in the tent if a student, on an average, occupies 5/7 m2 on the ground?

A cloth having an area of 165 m2 is shaped into the form of a conical tent of radius 5m.

Find the volume of the cone.

Find the volume and surface area of a sphere whose radius is:

3.5 cm

Find the volume and surface area of a sphere whose radius is:

4.2 cm

Find the volume and surface area of a sphere whose radius is:

5m

The volume of a sphere is 38808 cm3. Find its radius and hence its surface area.

Find the surface area of a sphere whose volume is 606.375m3.

Find the volume of a sphere whose surface area is 154 cm2.

The surface area of sphere is (576π) cm2. Find its volume.

How many lead shots, each 3mm in diameter, can be made from a cuboid with dimensions (12cm × 11cm× 9cm)?

How many lead balls, each of radius 1cm, can be made from a sphere of radius 8cm?

A solid sphere of radius 3cm is melted and then cast into smaller spherical balls, each of diameter 6cm. Find the number of small balls thus obtained.

A metallic sphere of radius 10.5cm is melted and then recast into smaller cones, each of radius 3.5cm and height 3cm. How many cones are obtained?

How many spheres 12cm in diameter can be made from a metallic cylinder of diameter 8cm and height 90cm?

The diameter of a sphere is 6cm. It is melted and drawn into a wire of diameter 2mm. Find the length of the wire.

The diameter of a copper sphere is 18cm. It is melted and drawn into a long wire of uniform cross section. If the length of the wire is 108m, find its diameter.

A sphere of diameter 15.6cm is melted and cast into a right circular cone of height 31.2cm. Find the diameter of the base of the cone.

A spherical cannonball 28cm in diameter is melted and cast into a right circular cone mould, whose base is 35cm in diameter. Find the height of the cone.

A spherical ball of radius 3cm is melted and recast into three spherical balls. The radii of two of these balls are 1.5cm and 2cm. Find the radius of the third ball.

The radii of two spheres are in the ratio 1:2. Find the ratio of their surface areas.

The surface areas of two spheres are in the ratio 1:4. Find the ratio of their volumes.

A cylindrical tub of radius 12cm contains water to a depth of 20cm. A spherical iron ball is dropped into the tub and thus the level of water is raised by 6.75cm. What is the radius of the ball?

A cylindrical bucket with base radius 15cm is filled with water up to a height of 20cm. A heavy iron spherical ball of radius 9cm is dropped into the bucket to submerge completely in the water. Find the increase in the level of water.

The outer diameter of a spherical shell is 12cm and its inner diameter is 8cm. Find the volume of metal contained in the shell. Also, find its outer surface area.

A hollow spherical shell is made of a metal of density 4.5g per cm3. If its internal and external radii are 8cm and 9cm respectively, find the weight of the shell.

A hemisphere of lead of radius 9cm is cast into a right circular cone of height 72cm. Find the radius of the base of the cone.

A hemispherical bowl of internal radius 9cm contains a liquid. This liquid is to be filled into cylindrical shaped small bottles of diameter 3cm and height 4cm. How many bottles are required to empty the bowl?

A hemispherical bowl is made of steel 0.5cm thick. The inside radius of the bowl is 4cm. Find the volume of steel used in making the bowl.

A hemispherical bowl is made of steel 0.25cm thick. The inner radius of the bowl is 5cm. Find the outer curved surface area of the bowl.

A hemispherical bowl made of brass has inner diameter 10.5cm. Find the cost of tin-plating it on the inside at the rate of ₹ 32 per 100cm2.

The diameter of the moon is approximately one fourth of the diameter of the earth. What fraction of the volume of the earth is the volume of the moon?

Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of the hemisphere?