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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]

Solution:

Given, radius of metal sphere = 2 cm

Internal dimensions of rectangular box = 16 cm × 8 cm × 8 cm

Metal spheres are packed into rectangular box

16 spheres area filled with preservative liquid

We have to find the volume of the liquid.

Volume of rectangular box = length × breadth × height

Given, length = 16 cm

Breadth = 8 cm

Height = 8 cm

Volume = 16 × 8 × 8

= 1024 cm³

Volume of sphere = 4/3 πr³

Where r is the radius of the sphere

Given, r = 2 cm

Volume = 4/3 (3.14)(2)³

= 4/3 (3.14)(8)

= 100.48/3

= 33.49 cm³

Volume of 16 spheres = 16(33.49)

= 535.84 cm³

Volume of preservative liquid = volume of box - volume of 16 spheres

= 1024 - 535.84

= 488.16 cm³

Therefore, the volume of the preservative liquid is 488 cm³

✦ Try This: The radius of a sphere increased by 50 percent. By how many percent did the surface area of the sphere increase?

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 13

NCERT Exemplar Class 9 Maths Exercise 13.3 Problem 1

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]

Summary:

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. The volume of this liquid is 488 cm³

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