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 radius of the hemisphere if curved surface area of the hemisphere is 2562 sq cm.
A. $sqrt{frac{8967}{44}}$	B. $sqrt{frac{8965}{22}}$	C. $sqrt{frac{8967}{22}}$	D. none of these
Right Option : C
View Explanation

Question : 2

Find the lateral surface area of the hemisphere having the radius 12 cm.
A. $frac{6336}{7}$	B. $frac{6338}{7}$	C. $frac{6339}{7}$	D. $frac{6335}{7}$
Right Option : A
View Explanation

Question : 3

Find the lateral surface area of the hemisphere having the radius 9 cm.
A. $509.242;cm^{2}$	B. $509.142;cm^{2}$	C. $509.142;cm^{2}$	D. none of these
Right Option : C
View Explanation

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