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 __ m ^{3}.**

**(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 __ cm ^{3}**

**(vi) The edge of a cube is 7cm , then its total surface are (T.S.A) will be __ cm ^{2}**

**(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 cm ^{2}**

**(b) 48 cm ^{2}**

**(c) 8 cm ^{2}**

**(d) 16 cm ^{2}**

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

**(a) 162 cm ^{2}**

**(b) 48 cm ^{2}**

**(c) 25 cm ^{2}**

**(d) 81 cm ^{2}**

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 m ^{3}**

**(b) 96 m ^{3}**

**(c) 120 m ^{3}**

**(d) 14 m ^{3}**

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 cm ^{3})**

**(a) 500 cm ^{3}more**

**(b) 500 cm ^{3} less**

**(c) 13 cm ^{3} more**

**(d) 13 cm ^{3} 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 m ^{3})**

Sol :

#### QUESTION 9

**The volume ‘of a cube is 1331 m ^{3} . 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 cm ^{2} of cloth will be required to make its cover ?**

Sol :

#### QUESTION 14

**The area of the base of a rectangular box is 70 cm ^{2} and area of two adjacent faces are 50 cm^{2} and 35 cm^{2} , 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 m ^{2 }?**

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 m ^{2}**

Sol :

#### QUESTION 18

**Total surface area of a rectangular body is 5200 cm ^{2} . 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 m ^{2}, 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 m ^{2} , 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 m ^{3 }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 m ^{3} . 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 dcm ^{3} . 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 m ^{3} 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 cm ^{2}**

**(ii) cost of the total wood a! the rate of Rs 1 per cm ^{3}**

<hint>

Sol :