# KC Sinha Mathematics Solution Class 9 Chapter 15 Surface Areas and Volume exercise 15.1

Page 15.21

### EXERCISE 15.1

Type 1

#### QUESTION 1

Fill in the blanks

(i) If each side of a cube be made m times, then ratio of original and new surface ares will be __

(ii) Volume of 10m,  5m and 6m cuboid will be __ m3.

(iii) The edge and diagonal of a cube are in the ratio __

(iv) A cube of 1m long side is cut off from a cube off from a cube of 2m long side

(v) The edge of a cube is 10m , then its volume will be __ cm3

(vi) The edge of a cube is 7cm , then its total surface are (T.S.A) will be __ cm2

(vii) Number of faces in a cube is __

(viii) Total number of faces in a cuboid is __

(ix) Total number of edges in a cuboid is __

(x) Total number of edges in a cube is __

(xi) In a cube or a cuboid, number of vertices is __

(xii) Total number of diagonals in a cube or cuboid is __

#### QUESTION 2

(i) If the edge of a cube be doubled, the volume will be :

(a) 4 times

(b) 8 times

(c) 16 times

(d) 2 times

(ii) If each edge of a cube be three times, how much will the total surface area become? Choose the correct answer from the following :

(a) 3 times

(b) 6 times

(c) 9 times

(d) 12 times

(iii) Dimensions of a triangle are :

(a) one

(b) three

(c) two

(d) innumerable

(iv) Duster has dimensions :

(a) three

(b) one

(c) two

(d) four

(v) Line has dimension :

(a) one

(b) two

(c) three

(d) none of these

(vi) Point has dimension(s) :

(a) one

(b) two

(c) three

(d) none of these

(vii) If diagonal of a cube is x cm , then find its one edge

(viii) Ratio of the volume of two cubes is 8:27 . What will be the ratio of edges ?

Sol :

#### QUESTION 3

(i) A cube of 2cm edge is cut off into 8 cubes is 1 cm edge . What is their total surface area ?

(a) 24 cm2

(b) 48 cm2

(c) 8 cm2

(d) 16 cm2

(ii) A cube of 3cm edge is cut off into 27 cubes of 1cm edge. What is their total surface area ?

(a) 162 cm2

(b) 48 cm2

(c) 25 cm2

(d) 81 cm2

Sol :

#### QUESTION 4

A room is 12 m long, 4 m wide and 3 m high. Find the length of the longest bar that can be placed in the room ?

Sol :

#### QUESTION 5

If each edge of a cube is 10 cm , then f‌ind its total surface area (T.S.A) and volume

Sol :

#### QUESTION 6

The height of a square room of side 6 m is 4 m, which of the following is the volume of the air is :

(a) 24 m3

(b) 96 m3

(c) 120 m3

(d) 14 m3

Sol :

#### QUESTION 7

A boy went to purchase 2 litres of milk. The shopkeeper gave him one full rectangular bucket milk which is 20 cm long, 15 cm wide and 5 cm deep. How much less or more milk they boy got ? (1 litres=1000 cm3)

(a) 500 cm3more

(b) 500 cm3 less

(c) 13 cm3 more

(d) 13 cm3 less

Sol :

#### QUESTION 8

If a rectangular tank has length 20 cm , breadth 15 m and height 10 m . How much kilolitres of water can be stored in it ? (1 kilolitre=1 m3)

Sol :

#### QUESTION 9

The volume ‘of a cube is 1331 m3 . Find its edge

Sol :

#### QUESTION 10

A water tank is 4 m long and 3.5 m wide and it is f‌illed with water. To lower down the water level by 2 cm, how much water will have to be released ?

Sol :

#### QUESTION 11

A cuboid is 5 m long, 4 m wide and and 3 m high. Find its total surface area (T.S.A) and volume

Sol :

#### QUESTION 12

A water tank is in the shape of a cuboid with sides as 6.25 m , 4.20 m and 3.15 m .  Find the volume of water in the tank when it is completely filled .

Sol :

#### QUESTION 13

The measurements of a box are 48cm , 36cm and 28cm . Find the volume of the box . How many cm2 of cloth will be required to make its cover ?

Sol :

#### QUESTION 14

The area of the base of a rectangular box is 70 cm2 and area of two adjacent faces are 50 cm2 and 35 cm2 , find the volume of the box

Sol :

#### QUESTION 15

A room is 13m long , 11m wide and 8cm high . What will be the expenses of colouring the walls at the rate of 25 paise per m2 ?

Sol :

#### QUESTION 16

Two cubes of 8cm edge each are joined together , find the surface area of the resulting cuboid .

Sol :

#### QUESTION 17

A room is 7 m long , 6.5 m wide and 4.5 m high in which there is a 3 m ×1.4 m gate and 4 equal windows of size 2 m ×1 m . Find the cost of colouring of internal walls at the rate of Rs 1 per m2

Sol :

#### QUESTION 18

Total surface area of a rectangular body is 5200 cm2 . If length and breadth of the body is 40 cm and 30 cm respectively , find its height

Sol :

#### QUESTION 19

Total surface area of a cube is 1014 m2, find its height

Sol :

#### QUESTION 20

If a rectangular solid has length, breadth and height in the ratio 4:5:6 and its total surface area be 3700 m2 , then f‌ind its length, breadth and height .

Sol :

#### QUESTION 21

The length of a room is its breadth and four times of height and it has 5832 m3 air. Find the length of the room.

Sol :

TYPE 2

#### QUESTION 22

Length, breadth and diagonal of a cuboid are 60cm , 20cm and 65cm respectively , find its volume

Sol :

#### QUESTION 23

If the diagonal of cubical body is 7√3 m , find its total surface area and volume .

Sol :

#### QUESTION 24

A cuboid shape wooden piece 2.3 cm long  , 0.75 m wide and of some thickness is cut off from a wooden log. Its volume is 1.104 m3 . How many rectangular planks of size 2.3m×0.75m×0.04m can be cut off from this cuboid ?

Sol :

#### QUESTION 25

A rectangular solid body is 80 cm long , 75 cm wide and 36 cm high . Find the side of cubical body whose volume is equal to that of solid body.

<hint>

Sol :

#### QUESTION 26

Find the depth of a water tank whose base is a square of 5 m side . In this water tank , water of a tank can be accommodated whose length, breadth and height are respectively 7.5m , 4m and 2.5 m

<hint>

Sol :

#### QUESTION 27

A f‌ield is 15 m long and 12 m wide. A pit 8 m long , 2.5 m wide and 2 m deep is dug in a comer of the f‌ield and soil taken out is spread uniformly over the remaining area of the field . Find the height through which the level of the field has been raised ?

<hint>

Sol :

TYPE 3

#### QUESTION 28

In how many cubes of 1 cm edge , a cube of 5 cm edge can be divided ?

(a) 5

(b)10

(c) 25

(d) 125

Sol :

#### QUESTION 29

Find the depth of a pond whose base is a square of 5 m Side. This pond cantains as much water as a pond having length, breadth and height 10 m, 5 m and 4 m respectively .

Sol :

#### QUESTION 30

(i) A room is 30 dcm long, 20 dcm wide and 17 dcm high. If each student is given a space of 100 dcm3 . How many students can sit in the room ?

(ii) A cinema hall is 100 m long , 50 m wide and 18 m high . If one person requires 150 m3 of air , then f‌ind how many persons can sit in the hall ?

Sol :

TYPE 4

#### QUESTION 31

A closed box is made of 2.5cm thick wood . If external dimensions of the box be 1m , 60cm and 50cm , find the volume of the wood used in the box.

<hint>

Sol :

#### QUESTION 32

Lengths of the outer edges of a closed box are respectively 25cm , 23cm and 18m . If thickness of the wood be 2cm , then find

(i) the total internal surface and also fins the cost of painting the internal surface at the rate of 50 paise per cm2

(ii) cost of the total wood a! the rate of Rs 1 per cm3

<hint>

Sol :

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