The length and breadth of a rectangular field are in the ratio 9: 5. If the area of the field is 14580 square meters, find the cost of surrounding the field with a fence at the rate of ₹3.25 per meter. Solution:
A rectangle is 16 m by 9 m. Find a side of the square whose area equals the area of the rectangle. By how much does the perimeter of the rectangle exceed the perimeter of the square? Solution:
Two adjacent sides of a parallelogram are 24 cm and 18 cm. If the distance between longer sides is 12 cm, find the distance between shorter sides.
Rajesh has a square plot with the measurement as shown in the given figure. He wants to construct a house in the middle of the plot. A garden is developed around the house. Find the total cost of developing a garden around the house at the rate of ₹50 per m2.
A flooring tile has a shape of a parallelogram whose base is 18 cm and the corresponding height is 6 cm. How many such tiles are required to cover a floor of area 540 m2? (If required you can split the tiles in whatever way you want to fill up the comers).
An ant is moving around a few food pieces of different shapes scattered on the floor. For which food piece would the ant have to take a longer round?
The perimeter of a trapezium is 52 cm. If its non-parallel sides are 10 cm each and its altitude is 8 cm, find the area of the trapezium.
In the adjoining figure, the area enclosed between the concentric circles is 770 cm2. If the radius of the outer circle is 21 cm, calculate the radius of the inner circle.
A copper wire when bent in the form of a square encloses an area of 121 cm2. If the same wire is bent into the form of a circle, find the area of the circle.
From the given figure, find
(i) the area of ∆ ABC
(ii) length of BC
(iii) the length of altitude from A to BC
A rectangular garden 80 m by 40 m is divided into four equal parts by two cross-paths 2.5 m wide. Find
(i) the area of the cross-paths.
(ii) the area of the unshaded portion.
Each side of a rhombus is 13 cm and one diagonal is 10 cm. Find
(i) the length of its other diagonal
(ii) the area of the rhombus
The cross-section ABCD of a swimming pool is a trapezium. Its width AB = 14 m, depth at the shallow end is 1-5 m and at the deep end is 8 m. Find the area of the cross-section.
The area of a trapezium is 360 m2, the distance between two parallel sides is 20 m and one of the parallel sides is 25 m. Find the other parallel side.
Find the area of a rhombus whose side is 6.5 cm and altitude is 5 cm. If one of its diagonal is 13 cm long, find the length of the other diagonal.
From the given diagram, calculate
(i) the area of trapezium ACDE
(ii) the area of parallelogram ABDE
(iii) the area of triangle BCD.
The area of a rhombus is equal to the area of a triangle whose base and the corresponding altitudes are 24.8 cm and 16.5 cm respectively. If one of the diagonals of the rhombus is 22 cm, find the length of the other diagonal.
The area of a trapezium is 540 cm2. If the ratio of parallel sides is 7: 5 and the distance between them is 18 cm, find the lengths of parallel sides.
From the adjoining sketch, calculate
(i) the length AD
(ii) the area of trapezium ABCD
(iii) the area of triangle BCD
The Diagram of the adjacent picture frame has outer dimensions = 28 cm × 32 cm and inner dimensions 20 cm × 24 cm. Find the area of each section of the frame, if the width of each section is the same.
In the given quadrilateral ABCD, ∠BAD = 90° and ∠BDC = 90°. All measurements are in centimeters. Find the area of the quadrilateral ABCD.
The top surface of a raised platform is in the shape of a regular octagon as shown in the given figure. Find the area of the octagonal surface.
There is a pentagonal shaped park as shown in the following figure:
For finding its area Jaspreet and Rahul divided it in two different ways.
Find the area of this park using both ways. Can you suggest some other way of finding its area? Solution:
In the diagram, ABCD is a rectangle of size 18 cm by 10 cm. In ∆ BEC, ∠E = 90° and EC = 8 cm. Find the area enclosed by the pentagon ABECD.
Polygon ABCDE is divided into parts as shown in the given figure. Find its area if AD = 8 cm, AH = 6 cm, AG = 4 cm, AF = 3 cm and perpendiculars BF = 2 cm, CH = 3 cm, EG = 2.5 cm.
Fill in the following blanks:
|Volume of cuboid||Length||Breadth||Height|
|(i)||90 cm3||-||5 cm||3 cm|
|(ii)||-||15 cm||8 cm||7 cm|
|(iii)||62.5 m3||10 cm||5 cm||-|
A godown is in the form of a cuboid of measures 55 m × 45 m × 30 m. How many cuboidal boxes can be stored in it if the volume of one box is 1.25 m3?
A rectangular pit 1.4 m long, 90 cm broad, and 70 cm deep was dug and 1000 bricks of base 21 cm by 10.5 cm were made from the earth dugout. Find the height of each brick.
A milk tank is in the form of a cylinder whose radius is 1.4 m and the height is 8 m. Find the quantity of milk in liters that can be stored in the tank.
A closed box is made of 2 cm thick wood with an external dimension 84 cm × 75 cm × 64 cm. Find the volume of the wood required to make the box.
Two cylindrical jars contain the same amount of milk. If their diameters are in the ratio 3: 4, find the ratio of their heights.
The radius of the base of a right circular cylinder is halved and the height is doubled. What is the ratio of the volume of the new cylinder to that of the original cylinder?
A rectangular piece of a tin of size 30 cm × 18 cm is rolled in two ways, once along its length (30 cm) and once along with its breadth. Find the ratio of volumes of two cylinders so formed.
Water flows through a cylindrical pipe of internal diameter 7 cm at 5 m per sec. Calculate
(i) the volume in liters of water discharged by the pipe in one minute.
(ii) the time in minutes, the pipe would take to fill an empty rectangular tank of size 4 m × 3 m × 2.31 m.
Two cylindrical vessels are filled with milk. The radius of one vessel is 15 cm and the height is 40 cm, and the radius of other vessels is 20 cm and the height is 45 cm. Find the radius of another cylindrical vessel of height 30 cm which may just contain the milk which is in the two given vessels.
Find the total surface area of a solid cylinder of radius 5 cm and height 10 cm. Leave your answer in terms of n.
An aquarium is in the form of a cuboid whose external measures are 70 cm × 28 cm × 35 cm. The base, side faces, and back face are to be covered with colored paper. Find the area of the paper needed.
The internal dimensions of the rectangular hall are 15 m × 12 m × 4 m. There are 4 windows each of dimension 2 m × 1.5 m and 2 doors each of dimension 1.5 m × 2.5 m. Find the cost of whitewashing all four walls of the hall, if the cost of whitewashing is ₹5 per m2. What will be the cost of whitewashing if the ceiling of the hall is also whitewashed?
A swimming pool is 50 m in length, 30 m in breadth, and 2.5 m in depth. Find the cost of cementing its floor and walls at the rate of ₹27 per square meter.
The floor of a rectangular hall has a perimeter of 236 m. Its height is 4·5 m. Find the cost of painting its four walls (doors and windows be ignored) at the rate of Rs. 8.40 per square meter.
A cuboidal fish tank has a length of 30 cm, a breadth of 20 cm, and a height of 20 cm. The tank is placed on a horizontal table and it is three-quarters full of water. Find the area of the tank which is in contact with water.
The volume of a cuboid is 448 cm3. Its height is 7 cm and the base is a square. Find
(i) aside from the square base
(ii) the surface area of the cuboid.
The length, breadth, and height of a rectangular solid are in the ratio 5: 4: 2. If its total surface area is 1216 cm2, find the volume of the solid.
A rectangular room is 6 m long, 5 m wide and 3.5 m high. It has 2 doors of size 1·1 m by 2 m and 3 windows of size 1.5 m by 1.4 m. Find the cost of whitewashing the walls and the ceiling of the room at the rate of ₹5.30 per square meter.
A cuboidal block of metal has dimensions 36 cm by 32 cm by 0·25 m. It is melted and recast into cubes with an edge of 4 cm.
(i) How many such cubes can be made?
(ii) What is the cost of silver coating the surfaces of the cubes at the rate of ₹0·75 per square centimeter?
Three cubes of silver with edges 3 cm, 4 cm, and 5 cm are melted and recast into a single cube, find the cost of coating the surface of the new cube with gold at the rate of ₹3.50 per square centimeter?
The curved surface area of a hollow cylinder is 4375 cm2, it is cut along its height and formed a rectangular sheet of width 35 cm. Find the perimeter of the rectangular sheet.
A road roller has a diameter of 0.7 m and its width is 1.2 m. Find the least number of revolutions that the roller must take in order to level a playground of size 120 m × 44 m.
A company packages its milk powder in a cylindrical container whose base has a diameter of 14 cm and a height of 20 cm. The company places a label around the surface of the container (as shown in the figure). If the label is placed 2 cm from top and bottom, what is the area of the label?
The sum of the radius and height of a cylinder is 37 cm and the total surface area of the cylinder is 1628 cm2. Find the height and the volume of the cylinder.
The ratio between the curved surface and the total surface of a cylinder is 1: 2. Find the volume of the cylinder, given that its total surface area is 616 cm3.
The given figure has shown a metal pipe 77 cm long. The inner diameter of the cross-section is 4 cm and the outer one is 4.4 cm.Find its
(i) inner curved surface area
(ii) outer curved surface area
(iii) total surface area.
A square field of side 65 m and a rectangular field of length 75 m have the same perimeter. Which field has a larger area and by how much?
The shape of the top surface of the table is a trapezium. Find the area if its parallel sides are 1.5 m and 2.5 m and the perpendicular distance between them is 0.8 m.
The length and breadth of a hall of a school are 26 m and 22 m respectively. If one student requires 1.1 sq. m area, then find the maximum number of students to be seated in this hall.
It costs ₹936 to fence a square field at ₹7.80 per metre. Find the cost of levelling the field at ₹2.50 per square metre.
The area of a trapezium is 160 sq. cm. Lengths of parallel sides are in the ratio 1:3. If the smaller of the parallel sides is 10 cm in length, then find the perpendicular distance between them.
The area of a trapezium is 729 cm2 and the distance between two parallel sides is 18 cm. If one of its parallel sides is 3 cm shorter than the other parallel side, find the lengths of its parallel sides.
The diagonals of a rhombus are 16 m and 12 m, find:
(i) its area
(ii) length of a side
The area of a parallelogram is 98 cm2. If one altitude is half the corresponding base, determine the base and the altitude of the parallelogram.
Preeti is painting the walls and ceiling of a hall whose dimensions are 18 m × 15 m × 5 m. From each can of paint 120 m2 of the area is painted. How many cans of paint does she need to paint the hall?
A rectangular paper is size 22 cm × 14 cm is rolled to form a cylinder of height 14 cm, find the volume of the cylinder. (Take π = 22/7)
A closed rectangular wooden box has inner dimensions 90 cm by 80 cm by 70 cm. Compute its capacity and the area of the tin foil needed to line its inner surface.
The lateral surface area of a cuboid is 224 cm2. Its height is 7 cm and the base is a square. Find
(i) side of the square base
(ii) the volume of the cuboid.
The inner dimensions of a closed wooden box are 2 m by 1.2 m by 0.75 m. The thickness of the wood is 2.5 cm. Find the cost of wood required to make the box if 1 m3 of wood costs ₹5400.
A car has a petrol tank 40 cm long, 28 cm wide, and 25 cm deep. If the fuel consumption of the car averages 13.5 km per liter, how far can the car travel with a full tank of petrol?
The diameter of a garden roller is 1.4 m and it is 2 m long. How much area it will cover in 5 revolutions?
The capacity of an open cylindrical tank is 2079 m3 and the diameter of its base is 21m. Find the cost of plastering its inner surface at ₹40 per square meter.
A solid right circular cylinder of height 1.21 m and diameter 28 cm is melted and recast into 7 equal solid cubes. Find the edge of each cube.
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