Question

If the total surface area of sphere is 2400 sq. cm . What is the total surface area of solid hemisphere having same radius. *​

Answer 1

Given:-

• Total surface area of sphere = 2400cm²

• Radius of Hemisphere = Radius of Sphere

To Find:-

• Total surface area of solid hemisphere.

Formula Used:-

• ${\boxed{\bf{TSA\:of\:Sphere=4\pi r^2}}}$

• ${\boxed{\bf{TSA\:of\: Hemisphere=3\pi r^2}}}$

Solution:-

Firstly,

$\bf :\implies\:TSA\:of\:Sphere=4\pi r^2$

$\sf :\implies\:2400=4\times \dfrac{22}{7}\times r^2$

$\sf :\implies\:2400=\dfrac{88}{7}\times r^2$

$\sf :\implies\:r^2=\dfrac{2400\times 7}{88}$

$\sf :\implies\:r^2=\dfrac{600\times 7}{22}$

$\sf :\implies\:r^2=\dfrac{300\times 7}{11}$

$\bf :\implies\:r^2=\dfrac{2100}{11}\:cm$

Now,

$\bf :\implies\:TSA\:of\: Hemisphere=3\pi r^2$

$\sf :\implies\:TSA\:of\: Hemisphere=3\times \dfrac{22}{7} \times \dfrac{2100}{11}$

$\sf :\implies\:TSA\:of\: Hemisphere=3\times 2\times 300$

$\bf :\implies\:TSA\:of\: Hemisphere=1800\:cm^2$

Hence, The Total Surface Area of the Hemisphere is 1800cm².

━━━━━━━━━━━━━━━━━━━━━━━━━