Total Surface Area of Hemisphere


 
 
Concept Explanation
 

Total Surface Area of Hemisphere

Total Surface Area of Hemisphere: The total surface area of Hemisphere of radius r is given by

2{pi}r^{2}+{pi}r^{2}=3{pi}r^{2};square;units

Illustration: Find the surface area and total surface area of a hemisphere each of radius 10cm. (Use ;{pi}=3.14).

Solution: We have, r = 10cm

Surface Area =2{pi}r^{2}=2times{3.14}times{10}times{10}=628;cm^{2

Total Surface Area = 3{pi}r^{2}=3times{3.14}times{10}times{10}=942;cm^{2}

Illustration:  The radius of a hemispherical balloon increases from 7 cm to 14 cm as air is being pumped into it. Find the ratios of the surface areas of the balloon in the two cases.

Solution:  Let S_{1} and S_{2} be the surface areas of the hemispherical balloon when its radii are 7 cm and 14 cm respectively. Then,

S_{1}=3pi times 7^{2}

S_{2}=3pi times (14)^{2}

therefore frac{S_{1}}{S_{2}}=frac{3pi times (7)^{2}}{3pi times (14)^{2}}

therefore frac{S_{1}}{S_{2}}=frac{ (7)^{2}}{(14)^{2}}

therefore frac{S_{1}}{S_{2}}=frac{ 1}{4}

Rightarrow S_{1}:S_{2}=1:4

Sample Questions
(More Questions for each concept available in Login)
Question : 1

Find the total surface are of a hemisphere of radius 16 cm.

Right Option : B
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Explanation
Question : 2

A cone hemisphere and a cylinder stands on equal bases and have the same height, the height being equal to the radius of the circular base, then their whole surface areas in the ratio.

Right Option : A
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Explanation
Question : 3

The total surface area of a hemispherical solid having radius 14 cm is ______________________

Right Option : B
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Explanation
 
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