# RD SHARMA Solutions for Class 9 Maths Chapter 18 - Surface Areas and Volume of a Cuboid and Cube

## Chapter 18 - Surface Areas and Volume of a Cuboid and Cube Exercise Ex. 18.1

Ravish wanted to make a temporary shelter for his car, by making a box-like structure with tarpaulin that covers all the four sides and the top of the car (with the front face as a flap which can be rolled up). Assuming that the stitching margins are very small, and therefore negligible, how much tarpaulin would be required to make the shelter of height 2.5 m, with base dimensions 4 m x 3m?

Breadth of shelter = 3 m

Height of shelter = 2.5 m

The tarpaulin will be required for top and four sides of the shelter.

Area of Tarpaulin required = 2(lh + bh) + lb

= [2(4 2.5 + 3 2.5) + 4 3] m

^{2}

= [2(10 + 7.5) + 12] m

^{2}

= 47 m

^{2}

An open box is made of wood 3 cm thick. Its external length, breadth and height are 1.48m, 1.16 m and 8.3 dm. Find the cost of painting the inner surface at Rs 50 per sq meter.

^{2}. How many bricks of dimensions 22.5 cm × 10 cm × 7.5 cm can be painted out of this container?

= [2(22.5 × 10 + 10 × 7.5 + 22.5 × 7.5)]cm

^{2}

= 2(225 + 75 + 168.75)

= (2 × 468.75) cm

^{2}

= 937.5 cm

^{2}

Let n number of bricks be painted by the container.

Area of n bricks = 937.5n cm

^{2}

Area that can be painted by the container = 9.375 m

^{2}= 93750 cm

^{2}

93750 = 937.5n

n = 100

Thus, 100 bricks can be painted out by the container.

The cost of preparing the walls of a room 12 m long at the rate of Rs 1.35 per square meter is Rs 340.20 and the cost of matting the floor at 85 paise per square meter is Rs 91.80. Find the height of the room.

^{2}and the rate of painting is 10 paise per cm

^{2}, find the total expenses required for polishing and painting the surface of the bookshelf.

External breadth (b) of bookshelf = 25 cm

External height (h) of bookshelf = 110 cm

External surface area of shelf while leaving front face of shelf

= lh + 2 (lb + bh)

= [85 110 + 2 (85 25 + 25 110)] cm

^{2}

= 19100 cm

^{2}

Area of front face = [85 110 - 75 100 + 2 (75 5)] cm

^{2}

= 1850 + 750 cm

^{2}

= 2600 cm

^{2}

Area to be polished = (19100 + 2600) cm

^{2}= 21700 cm

^{2}

Cost of polishing 1 cm

^{2}area = Rs 0.20

Cost of polishing 21700 cm

^{2}area = Rs (21700 0.20) = Rs 4340

Now, length (l), breadth (b) height (h) of each row of bookshelf is 75 cm, 20 cm, and

Area to be painted in 1 row = 2 (l + h) b + lh

= [2 (75 + 30) 20 + 75 30] cm

^{2}

= (4200 + 2250) cm

^{2}

= 6450 cm

^{2}

Area to be painted in 3 rows = (3 6450) cm

^{2}= 19350 cm

^{2}

Cost of painting 1 cm

^{2}area = Rs 0.10

Cost of painting 19350 cm

^{2}area = Rs (19350 0.10) = Rs 1935

Total expense required for polishing and painting the surface of the bookshelf

## Chapter 18 - Surface Areas and Volume of a Cuboid and Cube Exercise Ex. 18.2

^{3}= 135 m

^{3}

1 m

^{3}= 1000 litres

Thus, the tank can hold 135000 litres of water.

Length (l) of vessel = 10 m

Width (b) of vessel = 8 m

Volume of vessel = 380 m

^{3}

l b h = 380

10 8 h = 380

h = 4.75

Thus, the height of the vessel should be 4.75 m.

^{3}.

Width (b) of the cuboidal pit = 6 m

Depth (h) of the cuboidal pit = 3 m

Volume of the cuboidal pit = l b h = (8 6 3) = 144 m

^{3}

Cost of digging 1 m

^{3}= Rs 30

Cost of digging 144 m

^{3}= Rs (144 30) = Rs 4320

Breadth (b) of the cuboidal tank = 15 m

Height (h) of the cuboidal tank = 6 m

Capacity of tank = l × b × h = (20 × 15 × 6) m

^{3}= 1800 m

^{3}= 1800000 litres

Water consumed by people of village in 1 day = 4000 × 150 litres = 600000 litres

Let water of this tank lasts for n days.

Water consumed by all people of village in n days = capacity of tank

n × 600000 = 1800000

n = 3

Thus, the water of tank will last for 3 days.

A child playing with building blocks, which are of the shape of the cubes, has built a structure as shown in fig. If the edge of each cube is 3 cm, find the volume of the structure built by the child

Breadth of the godown = 25 m

Height of the godown = 10 m

Volume of godown = l

_{1}b

_{1}h

_{1}= (40 25 10) = 10000

Length of a wooden crate = 1.5 m

Breadth of a wooden crate = 1.25 m

Height of a wooden crate = 0.5 m

Volume of a wooden crate = = (1.5 1.25 0.5) m3 = 0.9375

Let n wooden crates be stored in the godown.

Volume of n wooden crates = volume of godown

0.9375 n = 10000

Thus, 10666 wooden crates can be stored in godown.

A wall of length 10 m was to be built across an open ground. The height of the wall is 4 m and thickness of the wall is 24 cm. If this wall is to be built up with bricks whose dimensions are 24 cm x 12 cm x 8 cm, how many bricks would be required?

Depth (h) of river = 3 m

Width (b) of river = 40 m

Volume of water flowed in 1 min

Thus, in 1 minute 4000 = 4000000 litres of water will fall into the sea.

A rectangular container, whose base is a square of side 5 cm, stands on a horizontal table, and holds water upto 1 cm from the top. When a cube is placed in the water it is completely submerged, the water rises to the top and 2 cubic cm of water overflows. Calculate the volume of the cube and also the length of its edge.

## Chapter 18 - Surface Areas and Volume of a Cuboid and Cube Exercise 18.35

Three equal cubes are placed adjacently in a row. The ratio of the total surface area of the resulting cuboid to that of the sum of the surface areas of three cubes, is

(a) 7 : 9

(b) 49 : 81

(c) 9 : 7

(d) 27 : 23

The length, width and height of a rectangular solid are in the ratio of 3 : 2 : 1. If the volume of the box is 48 cm^{3}, the total surface area of the box is

(a) 27 cm^{2}

(b) 32 cm^{2}

(c) 44 cm^{2}

(d) 88 cm^{2}

Let,

Length = 3x,

Width = 2x

Height = x

Volume = 48 cm^{3}

L×W×H = 48 cm^{3}

3x × 2x × x = 48 cm^{3}

6x^{3} = 48 cm^{3}

x^{3} = 8 cm^{3}

x = 2 cm

Total Surface area

= 2(3x × 2x + 2x × x + 3x × x)

= 2(6x^{2} + 2x^{2} + 3x^{2})

= 2(11x^{2})

= 22x^{2}

= 22(4)

= 88 cm^{2}

Hence, correct option is (d).

If the areas of the adjacent faces of a rectangular block are in the ratio 2 : 3 : 4 and the volume is 9000 cm^{3}, then the length of the shortest edge is

(a) 30 cm

(b) 20 cm

(c) 15 cm

(d) 10 cm

## Chapter 18 - Surface Areas and Volume of a Cuboid and Cube Exercise 18.36

If each edge of a cube, of volume V, is doubled, then the volume of the new cube is

(a) 2 V

(b) 4 V

(c) 6 V

(d) 8 V

Let edge = a

Volume, V = a^{3}

If a' = 2a, then

V' = (a')^{3} = (2a)^{3} = 8a^{3}

V' = 8 V

Hence, correct option is (d).

If each edge of a cuboid of surface area S is doubled, then surface area of the new cuboid is

(a) 2 S

(b) 4 S

(c) 6 S

(d) 8 S

The area of the floor of a room is 15 m^{2}. If its height is 4 m, then the volume of the air contained in the room is

(a) 60 dm^{3}

(b) 600 dm^{3}

(c) 6000 dm^{3}

(d) 60000 dm^{3}

The cost of constructing a wall 8 m long, 4 m high and 20 cm thick at the rate of Rs. 25 per m^{3} is

(a) Rs. 16

(b) Rs. 80

(c) Rs. 160

(d) Rs. 320

10 cubic metres clay is uniformly spread on a land of area 10 ares. The rise in the level of the ground is

(a) 1 cm

(b) 10 cm

(c) 100 cm

(d) 1000 cm

Volume of a cuboid is 12 cm^{3}. The volume (in cm^{3}) of a cuboid whose sides are double of the above cuboid is

(a) 24

(b) 48

(c) 72

(d) 96

Let the dimensions of Cuboid be a, b, c respectively.

Volume, V = abc = 12 cm^{3}

If a' = 2a, b' = 2b, c' = 2c, then

V' = a'b'c' = 8abc = 8 × 12 = 96 cm^{3}

Hence, correct option is (d).

If the sum of all the edges of a cube is 36 cm, then the volume (in cm^{3}) of that cube is

(a) 9

(b) 27

(c) 219

(d) 729

Let the edge of cube = a

Total no. of edge = 12

Sum of all edges = 12a

12a = 36cm

i.e. a = 3 cm

Volume = a^{3} = 3^{3} = 27 cm^{3}

Hence, correct option is (b).

The number of cubes of sides 3 cm that can be cut from a cuboid of dimensions 10 cm × 9 cm × 6 cm, is

(a) 9

(b) 10

(c) 18

(d) 20

On a particular day, the rain fall recorded in a terrace 6 m long and 5 m broad is 15 cm. The quantity of water collected in the terrace is

(a) 300 litres

(b) 450 litres

(c) 3000 litres

(d) 4500 litres

If each edge of a cube is increased by 50%, the percentage increase in its surface area is

(a) 50%

(b) 75%

(c) 100%

(d) 125%

## Chapter 18 - Surface Areas and Volume of a Cuboid and Cube Exercise 18.37

A cube whose volume is 1/8 cubic centimeter is placed on top of a cube whose volume is 1 cm^{3}. The two cubes are then placed on top of a third cube whose volume is 8 cm^{3}. The height of the stacked cubes is

(a) 3.5 cm

(b) 3 cm

(c) 7 cm

(d) none of these

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