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Question 1

A square and a rectangular field with measurements as given in the figure have equal perimeter. Which field has larger area?


Area of Square = 60 × 60 = 3600m2

Area of Rectangle = 40 × 80 = 3200m2

Square has larger area.

Question 2

Mrs Karshik has a square plot with the measurement as shown in the figure. She want 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 Rs. 55 per m2.

Area of a square plot = 25 × 25 = 625

Area of a garden = 625 − (15 × 20)

Garden area = 625 − 300 = 325

Cost of developing garden area = 325 × Rs. 55 = Rs. 17,875

Cost of developing garden area= Rs. 17,875.

Question 3

The shape of garden is rectangular in the middle and semi circles at the ends as shown in the diagram. Find the area of this garden and  the perimeter of this garden.

[Length of rectangle is 20 - (3.5+3.5) metres].

Area of the rectangular part = length x breadth
= 20 x 7 = 140 sq m
Area of Semicircular portions: = п x r2

Perimeter of the shape = 22 + 20 + 20 = 62 metres

Question 4

A flooring tile has the shape of a parallelogram whose base is 24cm and the corresponding height is 10cm. How many such titles are required to cover a floor of area 1080m2.


Area of parallelogram tile

Floor area = 1080 m2 = 1080 × 100 × 100 cm2.

Number of tiles required = = 45000.

Question 5

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? Circumference of a circle can be obtained by using the expression where r is the radius of the circle.


Perimeter of (1) is =

Perimeter of (2) is = Sum of three sides + Perimeter of semicircle

                          = 1.5 + 1.5 + 2.8 +



Perimeter of (3) is = 2 + 2 + 4.4 = 8.396

Ant have to take longer round in the diagram(2).

Question 6

The shape of the top surface of a table is a trapezium. Find its area if its parallel sides are 1m and 1.2 m and perpendicular distance between them is 0.8m.


Area of Trapezium


Question 7

The area of a trapezium is 34cm2 and the length of one of the parallel side is 10cm and its height is 4cm. Find the length of the other parallel side.

  • Solution:
    Area of a trapezium = 34cm2

    The length of the other parallel side = 7cm.

Question 8

Length of the fence of a trapezium shaped field ABCD is 120m. If BC = 48m. CD = 17m, AD = 40m. Find the area of the field. Side AB is perpendicular to the parallel sides AD and BC.

Draw perpendicular OD to BC.

OC = 8m, CD = 17m,

Area of trapezium

Area of the field = 660 m2.

Question 9

The diagonal of a quadrilateral shaped field is 24m and the perpendicular dropped on it from the remaining opposite vertices are 8m and 13m. Find the area of the field.


Area of a quadrilateral                


Area of the field = 252 m2.

Question 10

The diagonals of a rhombus are 7.5cm and 12cm. Find its area.

Area of a rhombus


Area of the rhombus = 45 cm2.

Question 11

Find the area of a rhombus whose diagonals are 6 cm and 8 cm in length?


Area of a rho


Question 12

The floor of a building consists of 3000 tiles which are rhombus shaped and each of its diagonals are 45cm and 30cm in length. Find the total cost of polishing the floor if the cost per m2 is Rs. 4.

Area of a rhombus


No of tiles = 3000

Polish Area = 3000 × .0675 = 202.5

Cost/m2 = Rs. 4

Total cost = 202.5 × 4 = Rs. 810.

Question 13

Mohan wants so buy a trapezium shaped field.Its side along the oliver is parallel to and twice the side along the road. If the area of this field is 10500m2 and the perpendicular distance between the two parallel sides is 100m. Find the length of the side along the river.



Area of a trapezium = 10500m2.

× (sum of parallel sides) × h = 10500

(Sum of parallel sides) × 100 = 10500

Sum of parallel sides = a + b. Since one side is twice the other a = 2b.

Length of the side along the river = 140m.

Question 14

Top surface of a revised platform is in the shape of a regular octagon as shown in the figure. Find the area of the octagonal surface.



Area of rectangle =

Area of trapezium


Area of octagonal surface = Area of a rectangle + 2 area of trapezium

   = 55 + 64 = 119 cm2.

Question 15

There is a pentagonal shaped park as shown in the figure. For finding its area Jyoti and Kavitha divided in two different ways. How did Jyothi and Kavitha find the area of the park?

Jyoti's way = area of two trapeziums      


Karitha's way = area of triangle + area of square

Question 16

Diagram of the adjacent picture frame has outer dimensions = 24cm × 28cm.

And inner dimensions = 16cm × 20cm. Find the area of each section of the frame if the width of each section is same.


Question 17

The are two cuboidal boxes as shown in the adjoining figure. Which box requires the lesser amount of material to make?

From (fig (a))

The total surface area


From fig(b)

The total surface area

Figure (a) requires the lesser amount of material.

Question 18

A suitcase with measures 80cm × 48cm × 24cm is to be with a tarpaulin cloth. How many metres of tarpulin of width 96cm is required to cover 100 such suit cases?


Surface area of a suitcase


Surface area of 100 suit cases

Width of the cloth                 = 96 cm.

To cover 100 suitcase

            Since 1m = 100cm.

144m tarpulin requires to cover 100 suit cases.

Question 19

Find the sides of a cube whose surface area is 600cm2.

Surface area of a cube = 600cm2.


Question 20

Rukhsar painted the outside of the cabinet of measure 1m × 2m × 1.5m. How much surface area did she cover if she painted all except the bottom of the cabinet?

Total surface area of the cabinet

Except the bottom of the cabinet = T.S.A -

                                               =13 - 2 = 11m2.

Question 21

Daniel is painting the walls and ceiling of a cuboidal hall with length, breadth and height of 15m, 10m and 7m respectively. From each can of paint 100m2 of area is painted. How many cans of paint will she need to paint the room?


Total surface area of the hall


Painting needed area = Walls + Ceiling - Base area


1 can of paint = 100m2.

For 500m2 area, Daniel need 5 cans of paints.

Question 22

Describe how the two figures are alike and how they are different. Which box has larger lateral surface area?

Two figures are alike:

The height of cylinder and cube are the same = 7cm.

Two figures are different:

The base area of the cylinder is circle in shape = 154 cm2.

The base area of the cube is square in shape = 49 cm2.

Lateral surface area of a cylinder


Lateral surface area of a cube

Cube has larger lateral surface area.

Question 23

A closed cylindrical tank of radius 7m and height 3m is made from a sheet of metal. How much sheet of metal is required.

Total surface area of the cylinder


Sheet of metal required = 440 m2.

Question 24

The lateral surface area of a hollow cylinder is 4224cm2. It is cut along its height and formed a rectangular sheet of width 33cm. Find the perimeter of rectangular sheet?

Given: Height of the hollow cylinder = 33cm.

Lateral surface area

Perimeter of a rectangle


Perimeter of the rectangle = 322cm.

Question 25

A road roller takes 750 complete revolutions to move once over to level a road. Find the area of the road if the diameter of a road roller is 84cm and length 1m.

Diameter = 84cm

Radius = 42 cm = 0.42m, length = 1m.

Area covered = curved surface × Number of revolutions


Area of the leveled road = 1980 m2.

Question 26

A company packages its milk powder in cylindrical container whose base has a diameter of 14cm and height 20cm. Company places a label around the surface of the container. If the label is placed 2cm from top and bottom, what is the area of the label?

Lateral surface area of a cylinder


Label's lateral surface area

2 cm from top & bottom

                           = 176cm2.

Area of the label = (880 - 176) cm2 = 704cm2.

Question 27

Given a cylindrical tank, in which situation will you find surface area and in which situation volume.

(a) To find how much it can hold.

(b) Number of cement bags required to plaster it.

(c) To find the number of smaller tanks that can be filled with water from it. 9; 9; 9; 9; 9; 9; 9;

(a) Volume

(b) surface area

(c) volume.

Question 28

Diameter of cylinder A is 7cm, and the height 14cm. Diameter of cylinder B is 14cm and height is 7cm. Without doing any calculations can you suggest whose volume is greater? Verify it by finding the volume of both the cylinders. Check whether the cylinder with greater volume also has greater surface area?

Volume of A

Volume of B

∴ B has greater volume.

Surface area


Surface area B

Surface area of B is greater than A.

Question 29

Find the height of a cuboid whose base area is 180cm2 and volume is 900cm3?

Volume of a cuboid

Base area

Height of the cuboid = 5 cm.

Question 30

A cuboid is of dimensions 60cm × 54cm × 30cm. How many small cubes with side 6cm can be placed in the given cuboid.

Volume of a cuboid

Volume of cube

Number of cubes can be placed


450 cubes can be placed inside cuboid.

Question 31

Find the height of the cylinder whose volume is 1.54m3 and diameter of the base is 14cm?

Volume of a cylinder = 1.54m3


Height of the cylinder = 1m.

Question 32

A milk tank is in the form of cylinder whose radius is 1.5m and length is 7m. Find the quantity of milk in litres that can be stored in the tank?

Volume of a cylinder


Quantity of milk that can be stored in the tank = 49500l.

Question 33

If each edge of a cube is doubled.


(i) How many times will its surface area increase?

(ii) How many times will its volume increase?

Surface area of a cube =

If is doubled

Surface area increases by 4 times.

(ii) Volume of a cube

If is doubled, volume

Volume increases by 8 times.

Question 34

Water is pouring into a cubiodal reservoir at the rate of 60 litres per minute. If the volume of reservoir is 108m3. Find the number of hours it will take to fill the reservoir.

Volume of the reservoir

Time = 60 litres / min = 3600 li/hr

Number of hours required to fill the reservoir = 30 hrs.

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