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

Question 17 Mensuration Exercise 17.3

If the volume of a sphere is 179\frac{2}{3} , Finds its radius and surface area.

Solution:

The area that a sphere's outer surface covers in three dimensions is known as the surface area of the object. A sphere is a three-dimensional solid that resembles a circle in shape.

Given volume of the sphere is 179\frac{2}{3}

(4/3)π r3 =** 179\frac{2}{3} **= 539/3**

(4/3)×(22/7)×r3 = 539/3

r3 = (539×3×7)/(4×22×3)

r3 = 49×7/8

r3 = 7×7×7/(2×2×2)

Taking cube root on both sides, we get

r = 7/2 = 3.5 cm

Surface area of the sphere = 4π r2

= 4×(22/7)×(7/2)2

= 22×7

= 154 cm2

Hence the radius and the surface area of the sphere is 3.5 cm and 154 cm2 respectively.

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