Mathematics exemplar problems class 10 Solutions for Chapter 12 surface areas and volumes

A surahi is the combination of

The shape of a glass (tumbler) (see Fig. 12.3) is usually in the form of

A shuttle cock used for playing badminton has the shape of the combination of

A cone is cut through a plane parallel to its base and then the cone that is formed on one side of that plane is removed. The new part that is left over on the other side of the plane is called

Volume of two spheres are in the ratio 64 : 27. The ratio of their surface areas is

A mason construction a wall of dimensions 270 cm × 300 cm × 350 cm with the bricks each of size 22.5 cm × 11.25 cm × 8.75 cm and it is assumed that \frac{1}{8} space is covered by the mortar. Then the number of bricks used to construct the wall is

During conversion of a solid from one shape to another, the volume of new shape will

A right circular cylinder of radius r cm and height h cm (where h > 2r) just encloses

a sphere of diameter

If two solid hemispheres of same base radius r are joined together along their bases, then curved surface area of this new solid is

The diameters of the two circular ends of the bucket are 44 cm and 24 cm. The height of bucket is 35 cm. The capacity of bucket is

Choose the correct answer from the given four options:

A cylindrical pencil sharpened at one edge is the combination of

A plumbline (sahul) is the combination of (see Fig. 12.2)

The shape of a gilli, in the gilli-danda game (see Fig.), is a combination of _____

A metallic spherical shell of internal and external diameters 4 cm and 8 cm, respectively is melted and recast into the form a cone of base diameter 8cm. The height of the cone is

A solid piece of iron in the form of a cuboid of dimensions 49cm × 33cm × 24cm, is moulded to form a solid sphere. The radius of the sphere is

Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere is

The radii of the top and bottom of a bucket of slant height 45 cm are 28 cm and 7 cm respectively. The curved surface area of the bucket is

A medicine-capsule is in the shape of a cylinder of diameter 0.5 cm with two hemispheres stuck to each to its ends. The length of entire capsule is 2 cm. The capacity of the capsule is

In a right circular cone, the corss–section made by a plane parallel to the base is a

A solid ball is exactly fitted inside the cubical box of side a. The volume of the ball is 4/3πa³.

State whether the following statment is true or false.

The volume of the frustrum of cone is \frac{1}{3}\pi h\left[r_1^2+r_2^2-r_1r_2\right], where h is the vertical height of the frustrum and r₁ , r₂ are the radii of the ends.

Two identical solid hemispheres of equal base radius r cm are stuck together along their bases. The total surface area of the combination is 6πr².

A solid cylinder of radius r and height h is placed over other cylinder of same height and radius. The total surface area of the shape so formed is 4πrh + 4πr².

A solid cone of radius r and height h is placed over a solid cylinder having same base radius and height as that of a cone. The total surface area of the combined solid is πr[√(r² + h² +3r + 2h].

An open metallic bucket is in the shape of a frustrum of a cone, mounted on a hollow cylindrical base made of the same metallic sheet. The surface area of the metallic sheet used is equal to the curved surface area of frustrum of a cone + area of circular base + curved surface area of cylinder.

State whether the following statment is true or false.

The curved surface area of a frustrum of a cone is \pi l\left(\mathbf{r}_1+\mathbf{r}_2\right), where l=\sqrt{h^2+\left(r_1+r_2\right)^2}, r₁ , r₂ are the radii of the two ends of frustrum and h is vertical height.

The capacity of a cylindrical vessel with a hemispherical portion raised upward, at the bottom as shown in figure is \frac{πr^2}{3}(3h-2r)

Three metallic solid cubes whose edges are 3 cm, 4 cm and 5 cm are melted and formed into a single cube. Find the edge of the cube so formed.

A cone of radius 8 cm and height 12 cm is divided into two parts by a plane through the mid-point of its axis parallel to its base. Find the ratio of the volumes of two parts.

Two cones with same base radius 8 cm and height 15 cm are joined together along their bases. Find the surface area of the shape so formed.

An ice–cream cone full of ice–cream having radius 5 cm, and height 10 cm, as shown in figure. Calculate the volume of ice–cream, provided that its 1/6 part is left unfilled with ice–cream.

How many spherical lead shots each of diameter 4.2 cm can be obtained from a solid rectangular lead piece with dimensions 66 cm, 42 cm and 21 cm?

Find the number of metallic circular discs with 1.5 cm base diameter and of height 0.2 cm to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm.

Two solid cones A and B are placed in a cylindrical tube as shown in the figure. The ratio

of their capacities are 2 : 1. Find the volume of the remaining portion of the cylinder .

How many shots each having diameter 3 cm can be made from a cuboidal lead solid of dimensions 9cm × 11cm × 12cm?

A bucket is in the form of a frustum of a cone and holds 28.490 litres of water. The radii of the top and bottom are 28 cm and 21 cm, respectively. Find the height of the bucket.

From a solid cube of side 7 cm, a conical cavity of height 7 cm and radius 3 cm is hollowed out. Find the volume of the remaining solid.

Two identical cubes each of volume 64 cm³ are joined together end to end. What is the surface area of the resulting cuboid?

Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm, containing some water. Find the number of marbles that should be dropped into the beaker so that water level rises by 5.6 cm.

How many spherical lead shots of diameter 4 cm can be made out of a solid cube of lead whose edge measures 44 cm?

A wall 24 m long, 0.4 m thick and 6 m high is constructed with the bricks each of

dimensions 25 cm × 16 cm × 10 cm. If the mortar occupies 1/10th of the volume of the

wall, then find the number of bricks used in constructing the wall.

A milk container of height 16 cm is made of metal sheet in the form of a frustrum of a cone with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of milk at the rate of ₹22 per L, which the container can hold.

A cylindrical bucket of height 32 cm and base radius 18 cm is filled with sand. This bucket is emptied on the ground, and a conical heap of sand is formed. If the height of conical heap is 24 cm, find the radius and slant height of the heap.

A rocket is in the form of a right circular cylinder closed at the lower end and surmounted by a cone with the same radius as that of cylinder. The diameter and height of cylinder are 6 cm and 12 cm, respectively. If the slant height of the conical portion is 5 cm, then find the total surface area and volume of rocket. (Use π = 3.14)

A building is in the form of a cylinder surmounted by a hemispherical vaulted dome and contain 41\ \frac{19}{21}m^3 of air. If the internal diameter of dome is equal to its total height above the floor, find the height of the building.

A hemispherical bowl of internal radius 9 cm is full of liquid. The liquid is to be filled into cylindrical shaped bottles each of radius 1.5 cm and height 4 cm. How many bottles are needed to empty the bowl?

A solid right circular cone of height 120 cm and radius 60 cm is placed in a right circular cylinder full of water of height 180 cm such that it touches the bottom. Find the volume of water left in cylinder, if the radius of the cylinder is equal to the radius to the cone.

Water flows through a cylindrical pipe, whose inner radius is 1 cm at the rate of 80 cm per second in an empty cylindrical tank, the radius of whose base is 40 cm. What is the rise of water level in tank in half an hour?

The rain water from a roof of dimensions 22 m × 20 m drains into a cylindrical vessel having diameter of the base 2 m and height 3.5 m. If the rain water collected from the roof just fill the cylindrical vessel, then find the rainfall in cm.

A pen stand made of wood is in the shape of cuboid with four conical depressions and a cubical depression to hold the pens and pins respectively. The dimensions of cuboid are 10 cm, 5 cm, 4 cm. The radius of each of the conical depression is 0.5 cm and depth is 2.1 cm. The edge of the cubical depression is 3 cm. Find the volume of the wood in the entire stand.

A rectangular water tank of base 11 m × 6 m contains water upto a height of 5 m. If the water in the tank is transferred to a cylindrical tank of radius 3.5 m, find the height of the water level in the tank.

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

A heap of rice is in the form of a cone of diameter 9 m and height 3.5 m. How much canvas cloth is required to just cover the heap?

A factory manufactures 120000 pencils daily. The pencils are cylindrical in shape each of length 25 cm and circumference of base as 1.5 cm. Determine the cost of colouring the curved surfaces of the pencils manufactured in one day at Rs 0.05 per dm².

Water is flowing at the rate of 15 km/h through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time will the level of water in pond rise by 21 cm?

A solid iron cuboidal block of dimensions 4.4 m × 2.6 m × 1m is recast into a hollow cylindrical pipe of internal radius 30 cm and thickness 5 cm. Find the length of the pipe.

500 persons are taking a dip into a cuboidal pond which is 80 m long and 50 m broad. What is the rise of water level in the pond, if the average displacement of the water by a person is 0.04m³?

A solid metallic hemisphere of radius 8 cm is melted and recasted into a right circular cone of base radius 6 cm. Determine the height of the cone.

How many cubic centimetres of iron is required to construct an open box whose external dimensions are 36 cm, 25 cm and 16.5 cm provided the thickness of the iron is 1.5 cm. If one cubic cm of iron weighs 7.5 g, find the weight of the box.

The barrel of a fountain pen, cylindrical in shape, is 7 cm long and 5 mm in diameter. A full barrel of ink in the pen is used up on writing 3300 words on an average. How many words can be written in a bottle of ink containing one fifth of a litre?

16 glass sphere each of radius 2 cm are packed into cuboidal box of internal dimensions 16 cm × 8 cm × 8 cm and then the box is filled with water. Find the volume of water filled in the box.