Ex 13.6 NCERT Solutions Class 9 Chapter 13




The solutions to exercise 13.6 (from class 9th's maths NCERT book) are given below. The exercise has 8 questions which have been explained thoroughly with proper reasoning.

Circumference of the base of a cylinder = 132 cm

2 πr = 132

2 x (22/7) x r = 132

r= (132 x 7)/(44)

r= 21 cm


Volume 

=  Ï€ r 2 h

= (22/7) x 21 x 21 x 25

= 22 x 3 x 21 x 25

= 34650 cm 3

= (34650/1000) l

= 34.560 l


Volume of the pipe =



Volume of inner cylinder − Volume of the outer cylinder

= Ï€ (14)2 h  − Ï€ (12) 2 h

= Ï€ h [ (14)2  − (12)2]

= (22/7) x 35 x [ 26 x 2 ]     

{ using  (a)2  − (b)2  = (a+b)(a − b)}

= 22 x 5 x 52

= 5720 cm3


1 cm3 of pipe weighs = 0.6 g

5720 cm3  of pipe will weigh

= 0.6 x 5720

=> 3432 g or 3.432 kg


(i)Volume of rectangular soft drink can

= l x b x h

= 5 x 4 x 15

= 300  cm 3


(ii)Volume of the cylindrical soft drink can

=  Ï€ r 2 h

=  (22/7) x (7/2) 2 x 10

= 11 x 7 x 5

= 385 cm 3

Cylindrical container has more capacity by 85cm 3

CSA of cylinder

94.2 =  2 Ï€ r h

94.2 = 2 x (3.14) x (5) x r

(94.2) /(2 x 3.14 x 5) = r

r= (30) /10

r=3 cm


(ii) Volume of the cylinder

=  Ï€ r 2 h

= (22/7) x 3 x 3 x 5

= 3.14 x 45

= 141.3 cm 3

(i) Rs 20 is spent in painting a cylinder inner surface area of = 1 m 2

Rs 2200 will be spent on painting a cylinder whose inner surface area is

= 2200/20 

= 110 m 2

So, the inner curved surface area of the cylinder is 110 m 2

(ii) CSA = 2 π r h

110 = 2 x (22/7) x r x 10

11 x 7 = 44 x r

r= 7/4

r= 1.75 m

(iii) Volume of the cylinder

=  Ï€ r 2 h

= (22/7) x 1.75 x 1.75 x 10

= 22 x 0.25 x 1.75 x 10

= 11 x 5 x 1.75

= 1.75 x 55

= 96.25 m 3

= 96.25 kl


1 litre= 1000 m 3

Volume of cylinder

= 15.4 litres

= 15400 m 3


Ï€ r 2 h = 15400

(22/7) x r x r x 1 = 15400

r 2= (15400)/(7/22)

r 2= 700/7

r 2= 100

r=10 m

Area of sheet required 

= 2 π r h + π r 2

= π r (2 h + r)

= (22/7) x 10 x (2 + 10)

= 31.4 x 12

= 376.80 m 2


Radius of pencil = 3.5 mm

Radius of graphite = 0.5 mm

So, radius of wood = 3 mm

Height of the pencil = 14 cm

= 140 mm


Volume of the pencil

= π r 2 h

= 22/7 x 3.5 x 3.5 x 140

= 22 x 0.5 x 3.5 x 140

= 22 x 5 x 14 x 3.5 

= 5390 mm 3

Volume of the graphite

= π r 2 h

= 22/7 x 0.5 x0.5 x 140

= 22 x 0.25 x 20

= 110 mm 3



Volume of the wood = V of pencil - Volume of graphite

=5390 -  110

= 5280 mm 3

Volume of the cylindrical bowl

= π r 2 h

= 22/7 x 3.5 x 3.5 x 4

= 22 x 0.5 x 3.5 x 4

= 22 x 2 x 3.5

= 22 x 7

= 154 cm3



For 250 patient they will have prepare

= 154 x 250 cm3

= 38500 cm3

= 38500/1000 litres

= 38.5 litres