Page 15.43

### EXERCISE 15.2

**Type 1**

#### QUESTION 1

**Fill in the blanks :**

**(i) A right circular cylinder has radius 7 cm and height 5 cm, then area of its curved surface will be __**

**(ii) Height of a right circular cylinder is 7 m and diameter of its base is 10 m , volume of the cylinder will be __ m ^{3}**

**(iii) Diameter of a right circular cylinder is 7 cm and height is 5 cm. What will be its curved surface area ?**

#### QUESTION 2

**(i) A right circular cylinder has radius 7 cm and height 10 cm, what will be its curved surface area ?**

**(ii) The area of the base of a right circular cylinder is πa ^{2} cm^{2 }and height is b cmm , what will be its curved surface area ?**

Sol :

#### QUESTION 3

**The radius of the base of a right circular cylinder is 14 cm and height 30cm , then find the following for the cylinder :**

**(i) area of curved surface**

**(ii) total surface area**

**(iii) volume**

Sol :

#### QUESTION 4

**The area of curved surface of a right circular cylinder is 1056 cm ^{2} and diameter of its base is 28 cm , find the height of the cylinder.**

Sol :

#### QUESTION 5

**The curved surface area til it round pillar is 2200 cm ^{2} . If its height is 35 cm then find the diameter of the pillar.**

Sol :

#### QUESTION 6

**The curved surface of a right circular cylinder is 1760 cm ^{3 }and its radius is 14 cm . Find its length**

Sol :

#### QUESTION 7

**The diameter of a cylinder is 25cm and height 20cm . Find **

**(i) area of the curved surface**

**(ii) total surface area**

**(iii) volume of cylinder in litres**

Sol :

#### QUESTION 8

**What will be the expenses of digging a well of radius 3 m and depth 7 m at the rate of Rs 30 per m ^{3 }?**

Sol :

#### QUESTION 9

**The capacity of a cylindrical tank is 6160 m ^{3 }.If diameter of its base is 28 m, find the expenses of painting the internal curved surface of the tank at the rate Rs 2.80 per m^{2}**

Sol :

#### QUESTION 10

**A rectangular paper is 10 cm wide and 12π cm long and on folding around along its length, the two ends of the paper are brought together to form a right circular cylinder . Find the radius of the cylinder .**

Sol :

#### QUESTION 11

**A fight circular cylindrical hole of 1 m radius is cut out from a cubical wooden piece of 3 m edge . Find the volume of remaining wooden piece.**

Sol :

**TYPE 2**

#### QUESTION 12

**If volume of a cylinder is V, its curved surface area A and radius of the base is r , then prove that 2V=Ar**

Sol :

#### QUESTION 13

**The volume of a right circular cylinder is 2310 m ^{3 }and diameter of the base is 14 m , then find the curved surface area of the cylinder.**

Sol :

#### QUESTION 14

**The volume of a cylinder is 54cm ^{3 }and height is 16 cm, what will be its curved surface area ?**

Sol :

#### QUESTION 15

**The perimeter of the base of a right circular cylinder is 88 cm and height is 5 cm , what will be its curved surface area ?**

Sol :

#### QUESTION 16

**The curved surface of a right circular cylinder is 880 cm ^{2 }and height is 20 cm, find the volume of the cylinder.**

Sol :

#### QUESTION 17

**The volume of a cylinder is 448π cm ^{3 }and its height is 7 cm. Find its lateral surface area and total surface area.**

Sol :

#### QUESTION 18

**(a) The curved surface of a cylinder is 4400 cm ^{2 }and circumference of its base is 110 cm , find the volume of the cylinder **

**(b) The perimeter of the base of a cylinder is 132 cm and its height is 25 cm , find the volume of the cylinder.**

Sol :

#### QUESTION 19

**A rectangular piece of paper is 22cm long and 10cm wide . This piece of paper is folded along the length to make a cylinder . Find the volume of the cylinder .**

Sol :

#### QUESTION 20

**A rectangular sheet of aluminium foil is 44 cm long and 20 cm wide. A cylinder is formed by folding the foil along the length. Find the volume of the cylinder .**

Sol :

#### QUESTION 21

**Two cylinder vessels are filled with oil . One vessel is having radius 15 cm height 24 cm . Another vessel having radius and height as 10cm and 18cm respectively . Find the radius of the vessel whose height is 30cm and which is completely filled with the oil of both the vessels .**

Sol :

**TYPE 3**

#### QUESTION 22

**The radius of the base of a right circular cylinder is 4cm and height is 3cm . On melting this cylinder , how many right circular cylinder having radius 2cm and height can be made ?**

Sol :

#### QUESTION 23

**The ratio of radii of two right circular cylinder is 2:3 and ratio of their heights is 5:3 . Find the ratio of the volumes of these cylinders .**

Sol :

#### QUESTION 24

**The volume of a 14cm long cylinder is equal to the volume of a cube of edge 11cm . Find the radius of this cylinder .**

Sol :

#### QUESTION 25

**A piece of iron is in the shape of a right circular cylinder whose diameter is 1.5m and length 3.5m . Find the volume of the piece . This piece on being melted is made in the form of a bar , whose base is a square of 5cm side . Find the length of the bar.**

<hint>

Sol :

#### QUESTION 26

**A right circular cylinder has height 7cm and radius of base 12cm . How many cubical dice of 2cm edge can be made out of melting the cylinder ?**

<hint>

Sol :

#### QUESTION 27

**A cylindrical vessel filled with water has internal diameter 7.8cm and height 28cm . Its entire water is put in a rectangular tub whose base is a square of side 26cm . Find the height of water in the tub .**

<hint>

Sol :

**TYPE 4**

#### QUESTION 28

**Internal and external radii of a copper pipe are respectively 3cm and 5cm . On melting the pipe , a solid right circular cylinder of the same length is made . Find the radius of the cylinder.**

Sol :

#### QUESTION 29

**A cylindrical iron road roller as shown in figure below, is 1m long. Its inner diameter is 54cm and thickness of the iron sheet rolled into the road roller is 9cm . Find the weight of the roller , if 1cm ^{3 }iron weights 8gm (π=3.14)**

<fig>

<hint>

Sol :

#### QUESTION 30

**A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior . The diameter of a pencil is 7mm and the diameter of the graphite is 1mm . If the length of the pencil is 14cm . Find the **

**(i) volume of the graphite **

**(ii) volume of the wood**

**(iii) the weight of the whole pencil, if the specify gravity of the wood is 0.7 gm/cm ^{3} and that of the graphite is 2.1 gm/cm^{3}**

<fig>

<hint>

Sol :