# ML Aggarwal Solutions Class 10 Mathematics Solutions for Mensuration Exercise 17.3 in Chapter 17 - Mensuration

Question 14 Mensuration Exercise 17.3

If the ratio of the volumes of the two sphere is 125 : 64, find the ratio of their surface areas.

Solution:

The amount of space that a sphere can occupy is measured by its volume. If we take a circular disc, attach a string to its circumference, then rotate it along the string, we can create a circle on a piece of paper. This provides us a sphere-like form.

Given ratio of volume of two spheres = 125/64

(4/3)π r13/(4/3)π r23 = 125/64

r13/ r23 = 125/64

Taking cube root on both sides

r1/r2 = 5/4

Ratio of surface areas of the spheres =

4π r12/4π r22

= r12/r22

= 52/42

= 25/16

Hence the ratio of the surface areas is 25:16.

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