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# KC Sinha Mathematics Solution Class 9 Chapter 15 Surface Areas and Volume exercise 15.2

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 __ m3

(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 πa2 cm2 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 cm2 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 cm2 . 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 cm3 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 m3 ?

Sol :

#### QUESTION 9

The capacity of a cylindrical tank is 6160 m3 .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 m2

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 m3 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 54cm3 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 cm2 and height is 20 cm, f‌ind the volume of the cylinder.

Sol :

#### QUESTION 17

The volume of a cylinder is 448π cm3 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 cm2 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 1cm3 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/cm3 and that of the graphite is 2.1 gm/cm3

<fig>

<hint>

Sol :

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