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 m³air. 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 :