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16 glass spheres each of radius 2 cm are packed into a cuboidal box of internal dimensions 16 cm × 8 cm × 8 cm and then the box is filled with water. Find the volume of water filled in the box

Solution:

Given, 16 glass spheres are packed into a cuboidal box and then the box is filled with water.

Radius of each sphere is 2 cm

Internal dimension of the cuboidal box is 16 cm × 8 cm × 8 cm

We have to find the volume of water filled in the box.

Volume of sphere = (4/3)πr³

= (4/3)(22/7)(2)³

= (4/3)(22/7)8

= 33.52 cm³

Volume of 16 spheres = 16(33.52)

= 536.32 cm³

Volume of cuboidal box = length × width × height

= 16 × 8 × 8

= 16 × 64

= 1024 cm³

Volume of water filled in the box = volume of box - volume of 16 spheres

= 1024 - 536.32

= 487.68 cm³

Therefore, the volume of water filled in the box is 487.68 cm³.

✦ Try This: 12 glass spheres each of radius 4 cm are packed into a cuboidal box of internal dimensions 26 cm × 18 cm × 18 cm and then the box is filled with water. Find the volume of water filled in the box.

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 13

NCERT Exemplar Class 10 Maths Exercise 12.4 Problem 11

16 glass spheres each of radius 2 cm are packed into a cuboidal box of internal dimensions 16 cm × 8 cm × 8 cm and then the box is filled with water. Find the volume of water filled in the box

Summary:

16 glass spheres each of radius 2 cm are packed into a cuboidal box of internal dimensions 16 cm × 8 cm × 8 cm and then the box is filled with water. The volume of water filled in the box is 487.68 cm³

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