# Concise Class-9 Solids Surface Area and Volume of 3D ICSE Maths

**Concise Class-9 Solids** Surface Area and Volume of 3D ICSE ICSE Maths Solutions Chapter-21. We provide step by step Solutions of Exercise / lesson-21 **Solids** Surface Area and Volume of 3D ** **for ICSE **Class-9th Concise** Selina Mathematics by R K Bansal.

Our Solutions contain all type Questions with Exe-21 A, Exe-21 B, and Exe-21 C, to develop skill and confidence. Visit official Website **CISCE** for detail information about ICSE Board Class-9th Mathematics .

**Concise Class-9 Solids** Surface Area and Volume of 3D ICSE ICSE Maths Solutions Chapter-21

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**Exercise 21 A, Concise Class-9 Solids Surface Area and Volume of 3D ICSE ICSE Maths Solutions **

Question 1

The length breadth and height of a rectangular solid are in the ratio of 5 : 4 : 2 if the total surface area of 1216 cm². Find the length breadth and height of the solid

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Therefore, the length, breadth and height of rectangular solid are

Question 2

The volume of a cube is 729 cm^{3}. Find its total surface area.

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Question 3

The dimensions of a Cinema Hall are 100 m, 60 m and 15 m. How many persons can sit in the hall, if each requires 150 m^{3} of air?

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Question 4

75 persons can sleep in a room 25 m by 9.6 m. If each persons requires 16 m^{3} of air; find the height of the room.

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Question 5

The edges of three cubes of metal are 3 cm, 4 cm and 5 cm. They are melted and formed into a single cube. Find the edge of the new cube.

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Question 6

Three cubes, whose edges are x cm, 8 cm and 10 cm respectively, are melted and recasted into a single cube of edge 12 cm. Find ‘x’.

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Question 7

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

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Question 8

The cost of papering the four walls of a room at 75 paisa per square meter Rs. 240. The height of the room is 5 metres. Find the length and the breadth of the room, if they are in the ratio 5 : 3.

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Question 9

The area of a playground is 3650 m^{2}. Find the cost of covering it with gravel 1.2 cm deep, if the gravel costs Rs. 6.40 per cubic metre.

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**
**The area of the playground is 3650 m

^{2}and the gravels are 1.2 cm deep. Therefore the total volume to be covered will be:

3650 x 0.012 =43.8 m

^{3}.

Since the cost of per cubic meter is Rs. 6.40, therefore the total cost will be:

43.8 x Rs.6.40 = Rs.280.32

Question 10

A square plate of side ‘x’ cm is 8 mm thick. If its volume is 2880 cm^{3}; find the value of x.

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Question 11

The external dimensions of a closed wooden box are 27 cm, 19 cm and 11 cm. If the thickness of the wood in the box is 1.5 cm; find:

(i) Volume of the wood in the box;

(ii) The cost of the box, if wood costs Rs. 1.20 per cm^{3};

(iii) Number of 4 cm cubes that could be placed into the box.

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Question 12

A tank 20 m long, 12 m wide and 8 m deep is to be made of iron sheet. If it is open at the top. Determine the cost of iron-sheet, at the rate of Rs. 12.50 per metre, if the sheet is 2.5 m wide.

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Question 13

A closed rectangular box is made of wood of 1.5 cm thickness. The exterior length and breadth are respectively 78 cm and 19 cm, and the capacity of the box is 15 cubic decimetres. Calculate the exterior height of the box.

** ****Answer**

Let exterior height is h cm. Then interior dimensions are 78-3=75, 19-3=16 and h-3 (subtract two thicknesses of wood). Interior volume = 75 x 16 x (h-3) which must = 15 cu dm

Question 14

The square on the diagonal of a cube has an area of 1875 sq. cm. Calculate:

(i) The side of the cube.

(ii) The total surface area of the cube.

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Question 15

A hollow square-shaped tube open at both ends is made of iron. The internal square is of 5 cm side and the length of the tube is 8 cm. There are 192 cm^{3} of iron in this tube. Find its thickness.

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Question 16

Four identical cubes are joined end to end to form a cuboid. If the total surface area of the resulting cuboid as 648 m^{2}; find the length of edge of each cube.

Also, find the ratio between the surface area of resulting cuboid and the surface area of a cube.

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**Concise Class-9 Solids Surface Area and Volume of 3D ICSE ICSE Maths Solutions Exercise-21(B)**

Question 1

The following figure shows a solid of uniform cross-section. Find the volume of the solid. All measurements are in centimetres.

Assume that all angles in the figures are right angles.

** ****Answer**

The given figure can be divided into two cuboids of dimensions 6 cm, 4 cm, 3 cm, and 9 cm respectively. Hence, volume of solid

Question 2

A swimming pool is 40 m long and 15 m wide. Its shallow and deep ends are 1.5 m and 3 m deep respectively. If the bottom of the pool slopes uniformly, find the amount of water in litres required to fill the pool.

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Question 3

The cross-section of a tunnel perpendicular to its length is a trapezium ABCD as shown in the following figure; also given that:

AM = BN; AB = 7 m; CD = 5 m. The height of the tunnel is 2.4 m. The tunnel is 40 m long. Calculate:

(i) The cost of painting the internal surface of the tunnel (excluding the floor) at the rate of Rs. 5 per m^{2} (sq. metre).

(ii) The cost of paving the floor at the rate of Rs. 18 per m^{2}.

** **** ****Answer**

**The cross section of a tunnel is of the trapezium shaped ABCD in which AB = 7m, CD = 5m and AM = BN. The height is 2.4 m and its length is 40m.
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Question 4

Water is discharged from a pipe of cross-section area 3.2 cm^{2} at the speed of 5m/s. Calculate the volume of water discharged:

(i) In cm^{3} per sec.

(ii) In litres per minute.

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Question 5

A hose-pipe of cross-section area 2 cm^{2} delivers 1500 litres of water in 5 minutes. What is the speed of water in m/s through the pipe?

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Question 6

The cross-section of a piece of metal 4 m in length is shown below. Calculate:

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