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Maths / Surface Area and Volume / Lateral Surface Area of Hemisphere
(A Brief Glimpse of ABHYAS Content - Have aLook !!!!)

# 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

$\dpi{100} S=2{\pi}r^{2} \;square\;units$

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

$2\pi r=17.6$

$r=\frac{17.6}{2\pi}$

Now, $S=2\pi r^{2}$

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

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

$= \frac{(17.6)^{2}}{2\pi }$

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

$S= 49.28\;m^{2}$

Converting $\dpi{100} m^2\;\; into\;\; cm^2$

$S=49.28\times 10000\;cm^{2}$

$S=492800\;cm^{2}$

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

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

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

$=Rs\;24,640$

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