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