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