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NCERT Exemplar · Class 9 · Maths

Chapter 13: Surface Areas and Volumes

Practice each question, then open the answer or worked solution.

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Exercise 13.3

Textbook page 126 · 4 questions
Q1Written answer

Metal spheres, each of radius 2 cm, are packed into a rectangular box of internal dimensions 16 cm × 8 cm × 8 cm. When 16 spheres are packed the box is filled with preservative liquid. Find the volume of this liquid. Give your answer to the nearest integer. [Use π =3.14]

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Worked solution

According to the question,

Radius of each sphere, r = 2 cm

Volume of a sphere is given by

Volume of 1 sphere = 4/3 πr3

Since there are 16 spheres in our question,

Volume of 16 spheres = 16 × 4/3 πr3

= 16 × 4/3 × 3.14 × 23

= 535.89 cm3

We know that,

Dimensions of rectangular box = 16 cm × 8 cm × 8 cm

Volume of rectangular box = 16 × 8 × 8 = 1024 cm3

In order to find volume of the liquid that is filled in rectangular box,

We need to find the space left in the rectangular box after the space occupied by the spheres.

So, we can say that,

Volume of the liquid = (Volume of the rectangular box) – (Volume of the 16 spheres)

⇒ Volume of the liquid = 1024 – 535.89

= 488.11 cm3

Thus, volume of this liquid is 488.11 cm3.

Q2Written answer

A storage tank is in the form of a cube. When it is full of water, the volume of water is 15.625 m3.If the present depth of water is 1.3 m, find the volume of water already used from the tank.

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Worked solution

When the cubical tank is full:

Volume of water = Volume of cube = 15.625 m3

So, we know that,

Volume of cube = (length of edge of cube)3

⇒ (length of edge of cube)3 = 15.625

⇒ length of edge of cube = ∛15.625

= 2.5 m

We know that,

Length of the edge of the cube = 2.5 m.

When the present depth of the water is 1.3 m:

Length of tank = 2.5 m

Breadth of tank = 2.5 m

So, volume of water upto 1.3 m depth = length × breadth × depth

= 2.5 × 2.5 × 1.3

= 8.125 m3

Then, volume of water already used from the tank = (Volume of tank when it was full of water) –

(Volume of water when depth is 1.3 m)

= 15.625 – 8.125

= 7.5 m3

Thus, volume of water already used from the tank is 7.5 m3.

Q3Written answer

Find the amount of water displaced by a solid spherical ball of diameter 4.2 cm, when it is completely immersed in water.

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Worked solution

Water displaced when a solid spherical ball is immersed completely in water equals to its own volume.

According to the question,

Diameter of spherical ball = 4.2 cm

⇒ radius of spherical ball = 4.2/2 = 2.1 cm

So, volume of a sphere = 4/3 πr3

(4/3) (22/7)(2.1)3 = 38.81

Thus, volume of water displaced is 38.81 cm3.

Q4Written answer

How many square metres of canvas is required for a conical tent whose height is 3.5 m and the radius of the base is 12 m?

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Worked solution

According to the question,

Dimensions of conical tent are:

Height = 3.5 m

Radius = 12 m

Curved surface area of cone = πr√(r2 + h2)

= 22/7 × 12 √(122 + 3.52)

= 22/7 × 12 × √156.25

= 22/7 × 12 × 12.5

= 471.43 m2

Since, area of canvas = curved surface area of conical tent

Therefore, area of canvas required is 471.43 m2.