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 area of Hemisphere of radius 12.6 cm

Right Option : C
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Explanation
Question : 2

Find the total surface area of hemisphere if radius is 28 m.

Right Option : B
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Explanation
Question : 3

Find radius of the hemisphere if total surface area of the hemisphere is 5544 sq cm.

Right Option : C
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Explanation
 
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