# Question 1

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

**Solution:**

Area of Square = 60 Ã— 60 = 3600m

^{2}

Area of Rectangle = 40 Ã— 80 = 3200m^{2}

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 m**

^{2}.

**Solution:**

Area of a square plot = 25 Ã— 25 = 625

Area of a garden = 625 âˆ’ (15 Ã— 20)

Garden area = 625 âˆ’ 300 = 325

Cost of developing garden area = 325 Ã— 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].**

**Solution:**

^{2}

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 1080m**

^{2}.**Solution:**

Floor area = 1080 m^{2} = 1080 Ã— 100 Ã— 100 cm^{2}.

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.**

**Solution:**

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 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.**

**Solution:**

Draw perpendicular OD to BC.

OC = 8m, CD = 17m,

Area of trapezium

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

Area of the field = 660 m^{2}.

# Question 11

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

**Solution:**

Area of a rhombus

# 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 m**

^{2 }is Rs. 4.**Solution:**

Area of a rhombus

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

No of tiles = 3000

Polish Area = 3000 Ã— .0675 = 202.5

Cost/m^{2} = Rs. 4

Total cost = 202.5 Ã— 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 10500m**

^{2}and the perpendicular distance between the two parallel sides is 100m. Find the length of the side along the river.

**Solution:**

Area of a trapezium = 10500m^{2}.

Ã— (sum of parallel sides) Ã— *h* = 10500

(Sum of parallel sides) Ã— 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 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?**

**Solution:**

Jyoti's way = area of two trapeziums Â Â Â Â Â

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

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

# Question 17

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

**Solution:**

From (fig (a))

The total surface area

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

From fig(b)

The total surface area

Figure (a) requires the lesser amount of material.

# Question 18

**A suitcase with measures 80cm**

**Ã— 48cm Ã—**

**24cm is to be with a tarpaulin cloth. How many metres of tarpulin of width 96cm is required to cover 100 such suit cases?**

**Solution:**

Surface area of a suitcase

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

Surface area of 100 suit cases

Width of the clothÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 96 cm.

To cover 100 suitcase

Â Â Â Â Â Â Â Â Â Â Â Since 1m = 100cm.

144m tarpulin requires to cover 100 suit cases.

# Question 20

**Rukhsar painted the outside of the cabinet of measure 1m**

**Ã— 2m Ã—**

**1.5m. How much surface area did she cover if she painted all except the bottom of the cabinet?**

**Solution:**

Total surface area of the cabinet

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

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â =13 - 2 = 11m^{2}.

# 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 100m**

^{2}of area is painted. How many cans of paint will she need to paint the room?**Solution:**

Given

Total surface area of the hall

Â

Painting needed area = Walls + Ceiling - Base area

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

1 can of paint = 100m^{2}.

For 500m^{2} 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?**

**Solution:**

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 cm^{2}.

The base area of the cube is square in shape = 49 cm^{2}.

Lateral surface area of a cylinder

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

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.**

**Solution:**

Total surface area of the cylinder

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

Sheet of metal required = 440 m^{2}.

# Question 24

**The lateral surface area of a hollow cylinder is 4224cm**

^{2}. It is cut along its height and formed a rectangular sheet of width 33cm. Find the perimeter of rectangular sheet?**Solution:**

Given: Height of the hollow cylinder = 33cm.

Lateral surface area

Perimeter of a rectangle

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

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.**

**Solution:**

Diameter = 84cm

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

Area covered = curved surface Ã— Number of revolutions

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

Area of the leveled road = 1980 m^{2}.

# 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?**

**Solution:**

Lateral surface area of a cylinder

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

Label's lateral surface area

2 cm from top & bottom

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 176cm^{2}.

Area of the label = (880 - 176) cm^{2} = 704cm^{2}.

# 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; **

**Solution:**

(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?**

**Solution:**

Volume of A

Volume of B

âˆ´ B has greater volume.

Surface area

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

Surface area B

Surface area of B is greater than A.

# Question 30

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

**Solution:**

Volume of a cuboid

Volume of cube

Number of cubes can be placed

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

450 cubes can be placed inside cuboid.

# Question 33

**If each edge of a cube is doubled.**

Â

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

**(ii) How many times will its volume increase?**

**Solution:**

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 108m**

^{3}. Find the number of hours it will take to fill the reservoir.**Solution:**

Volume of the reservoir

Time = 60 litres / min = 3600 li/hr

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