NCERT Solutions Class 9 Chapter 13 Ex 13.5


The solutions to exercise 13.5 (from class 9th's maths NCERT book) are given below. The exercise has 9 questions which have been explained thoroughly with proper reasoning. 



Match box is a cuboid with length, l = 4 cm; breadth, b = 2.5 cm; and height, h= 1.5 cm

Volume of 1 matchbox 

= l x b x h

= 4 x 2.5 x 1.5

= 10 x 1.5

= 15 cm 3


Volume of 12 such matchboxes 

= 12 x 15

= 180 cm 3


Cuboidal water tank

l= 6 m , b= 5 m and h= 4.5 m

Volume of the cuboidal water tank

= l x b x h

= 6 x 5 x 4.5

= 30 x 4.5

= 135 m 3 = 135000 l


Cuboidal vessel

l= 10 m, b = 8 m, h= ?

Volume of the vessel = 380 m 3

 V = l x b x h

380 = 10 x 8 x h

380/80 = h

h= 4.75 m

Volume of the cuboidal pit

= l x b x h

= 8 x 6 x 3

= 144 m 3

Cost of digging 1 m 3 = Rs 30

Cost of digging 144 m 3  = 144 x 30 => Rs 4320

Cuboidal tank

l= 2.5 m , b=? , h = 10 m

Volume = 50,000 l

= (50,000/1000) m 3

= 50 m 3

V = l x b x h

50 = 2.5 x 10 x b

50 = 25 x b

b= 2 m

Water tank dimensions

l= 20 m, b= 15 m, h = 6 m




Volume of water consumed per day by 4000 people

= 4000 x 150 l

= (4000 x 150)/1000

= 600 m 3


Volume of the tank

= l xb x h

= 20 x 15 x 6

= 1800 m 3


600 m 3 water is consumed in 1 day

1800 m 3 water will be consumed in

= (1800)/600

=> 3 days


Volume of the Godown

= l x b x h

= 40 x 25 x 10

= 10, 000 m 3

Volume of 1 wooden crate

= l x b x h

= 1.5 x 1.25 x 0.5

= 0.9375 m 3




Number of crates that can be stored in the godown

= ( V of godown)/ ( V of 1 wooden crate)

= 10,000 / 0.9375

= 10,000 (approx)


Let the side of the new cube be n



Volume of original cube = 8 x volume of new cube

(12) 3 = 8 x (n) 3

(12) 3 = (2) 3 x (n) 3

12 = 2 x n

n= 6



The edge length of the new cube is 6 m

TSA of bigger cube 

= 6 x (l) 3

= 6 x (12) 3

TSA of smaller cube 

= 6 x (l) 3

= 6 x (6) 3

Ratio of the TSA

= {6 x (12) 3}/ 6 x (6) 3}

=> 8:1



Distance (length) that water moves in 60 minutes (1 hour) = 2000 m {1 km = 1000 m}

Distance (length) that water moves in 1 minutes (1 hour) = 2000/60 => 100/3 m

So we have to find the volume of the water column whose l= 100/3 m, b= 40 m and h= 3 m

= l x b x h

=  (100/3) x 40 x 3

= 4000 m 3