Question

Curved surface area of a solid hemispherical wooden block is 122cm^2.Find it's total surface area?​

Answer 1

Solution :-

CSA of a solid hemisherical wooden block = 122 cm²

Also CSA of hemisphere = 2πr² sq. units

⇒ 122 = 2πr²

⇒ 122/2 = πr²

⇒ 61 = πr²

TSA of hemisphere = 3πr² sq. units

= 3 * 61

[ Because πr² = 61 ]

= 183 cm²

Therefore TSA of solid hemispherical wooden block is 183 cm².

Answer 2

$\huge\mathbb{\underline{SOLUTION:-}}$

$\bf{Given:}\begin{cases}\sf{C.S A\:of\: Hemisphere=122cm{}^{2}}\end{cases}$

We have to find the T.S.A of hemisphere

$\boxed{\sf{C.S.A\:of\: Hemisphere=2\pi r{}^{2}}}$

$\boxed{\sf{T.S.A\:of\: Hemisphere=3\pi r{}^{2}}}$

Now

$\bf\underline{\red{According\:To\: Question:-}}$

First find the value of $\sf \pi r{}^{2}$

$\sf:\:\implies 2\pi r{}^{2}= 122\\ \\ \sf:\:\implies 2\times \pi r{}^{2}=122\\ \\ \sf:\:\implies \pi r{}^{2}=\cancel{\dfrac{122}{2}}\\ \\ \sf:\:\implies \pi r{}^{2}=61$

Now T.S.A of Hemisphere

$\sf\implies :\:\:\pi r{}^{2}= 61\\ \\ \sf:\:\implies T.S.A=3\pi r{}^{2}\\ \\ \sf:\:\implies T.S.A=3\times 61\\ \\ \sf:\:\implies T.S.A=183cm{}^{2}$

$\boxed{\sf{T.S.A\:of\: Hemisphere=183cm{}^{2}}}$