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

Question 22 Mensuration Exercise 17.3

The surface area of a solid sphere is 1256 cm². It is cut into two hemispheres. Find the total surface area and the volume of a hemisphere. Take π = 3.14.

Solution:

The space that a hemisphere takes up is referred to as its volume. The volume of a thing determines how much space it takes up. Half of a whole sphere, a hemisphere is a 3D object. As a result, a hemisphere's volume is equal to half that of a sphere.

Given surface area of the sphere = 1256 cm2

4π r2 = 1256

4×3.14×r2 = 1256

r2 = 1256×/3.14×4

r2 = 100

r = 10 cm

Total surface area of the hemisphere = 3π r2

= 3×3.14×102

= 3×3.14×100

= 942 cm2

Hence the total surface area of the hemisphere is 942 cm2.

Volume of the hemisphere = (2/3)π r3

= (2/3)×3.14×103

= (2/3)×3.14×1000

= (2/3)×3140

= 6280/3

= 2093\frac{1}{3}\ \ \ cm^3

Hence the volume of the hemisphere is 2093\frac{1}{3}\ \ \ cm^3

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