Lateral Surface Area of Hemisphere


 
 
Concept Explanation
 

Lateral Surface Area of Hemisphere

Lateral Surface Area of Hemisphere: The curved surface area of hemisphere is known as Lateral surface area of hemisphere. The Lateral surface area of hemisphere of radius r is given by

                                                      S=2{pi}r^{2} ;square;units

Illustration: A hemi-spherical dome of a building needs to be painted. If the circumference of the base of the dome is 17.6 m, find the cost of painting it, given the cost of painting is Rs 5 per 100;cm^{2}.

 

Solution: Given: Circumference of the base of the dome = 17.6 m and let S be the curved surface area of the dom.

 

As base of the dome is circular. So, we have

2pi r=17.6

r=frac{17.6}{2pi}

Now, S=2pi r^{2}

           =2pi times left ( frac{17.6}{2pi} right )^{2}

           =2pi times frac{(17.6)^{2}}{4pi ^{2}}

           = frac{(17.6)^{2}}{2pi }

          = frac{(17.6)^{2}times 7}{2times 22 }

S= 49.28;m^{2}

Converting m^2;; into;; cm^2

S=49.28times 10000;cm^{2}

S=492800;cm^{2}

As the cost of painting 100;cm^{2} = Rs 5

So, cost of painting 1;cm^{2} = 5div 100

 So, cost of painting 492800;cm^{2} = frac{5}{100}times 492800;cm^{2}

                                                    =Rs;24,640

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

Find the lateral surface area of the hemisphere having the radius 12 cm.

Right Option : A
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Explanation
Question : 2

Find the radius of the hemisphere if curved surface area of the hemisphere is 2562 sq cm.

Right Option : C
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Explanation
Question : 3

Find the lateral surface area of the hemisphere having the radius 9 cm.

Right Option : C
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Explanation
 
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