# ML Aggarwal Solutions Class 10 Mathematics Solutions for Mensuration Exercise 17.4 in Chapter 17 - Mensuration

Question 3 Mensuration Exercise 17.4

From a cube of edge 14 cm, a cone of maximum size is carved out. Find the volume of the remaining material.

Solution:

Assume that a cone has a height of "h" and a circular base with radius "r." This cone will have a volume that is one-third of the product of the base's area and its height.

Given edge of the cube, a = 14 cm

Radius of the cone, r = 14/2 = 7 cm

Height of the cone, h = 14 cm

Volume of the cube = a3

= 143

= 14×14×14

= 2744 cm3

Volume of the cone = (1/3)π r2h

= (1/3)×(22/7)×72×14

= 22×7×14/3

= 2156/3 cm3

Volume of the remaining material = Volume of the cube- Volume of the cone

= 2744-2156/3

= (3×2744-2156)/3

= (8232 – 2156)/3

= 6076/3

= 2025\ \frac{1}{3}\ cm^3

Hence the volume of the remaining material is 2025\ \frac{1}{3}\ cm^3

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