Question

if the base area of a hemispherical solid is 2386 square metre then find its curved surface area​

Answer 1

Answer:

37.48 m²

Step-by-step explanation:

$\underline{\bigstar\:\textsf{Given:}}$

• $\sf{Base\:area\:of\:a\:hemispherical\:solid\:=\:2386 m^2}$

$\underline{\bigstar\:\textsf{To\:find:}}$

• Curved surface area (CSA) = ?

$\underline{\bigstar\:\textsf{Solution:}}$

Hemisphere = The half of a sphere is hemisphere. The cross-section of hemisphere is a circle.

(Cross-section = If we cut any shape into to parts the upper view is known as cross-section.)

We know that the cross-section of hemisphere is a circle and we are given with the base area means the area of its cross-section. So, $\blue{\sf{The\:area\:of\:circle\:=\:\pi\:r^2}}$

(Let's find the radius of hemisphere first !)

$\longrightarrow\:\sf{2386\:=\:\dfrac{22\:×\:r^2}{7}}$

$\longrightarrow\:\sf{\dfrac{2386\:×\:7}{22}\:=\:r^2}$

$\longrightarrow$ 108.45 × 7 = r²

$\longrightarrow\:\sf{\sqrt{759.15}}$ = r

$\longrightarrow$ 27.55 = r

${\large{\boxed{\sf{\therefore \: radius\: 27.55\:m}}}}$

Now we know, $\blue{\sf{CSA\:of\:hemisphere\:=\:2\pi\:r^2}}$

$\implies\:\sf{CSA\:=\:\dfrac{2\:×\:22\:×\:(27.55)^2}{7}}$

$\implies\:\sf{CSA\:=\:\dfrac{44\:×\:759.0025}{7}}$

$\implies\:\sf{CSA\:=\:\dfrac{44\:×\:590025}{7\:×\:10000}}$

$\implies$ CSA = 44 × 8.42

$\implies$ CSA = 37.48 m²

${\large{\boxed{\sf{\therefore\:CSA\:of\:hemispherical\:solid\:is\:37.48\:m^2}}}}$

Hope it helped you dear...