The surface area of a solid sphere is 1256 cm². It is cut into two hemispheres. Find the total surface area and the volume of a hemisphere. Take π = 3.14

Given,
surface area of the sphere = 1256 cm².

We know that, surface area of sphere = 4πr².

∴ 4πr² = 1256

$\Rightarrow 4 \times 3.14 \times r^2 = 1256 \\[1em] \Rightarrow r^2 = \dfrac{1256}{3.14 \times 4} \\[1em] \Rightarrow r^2 = \dfrac{1256}{12.56} \\[1em] \Rightarrow r^2 = 100 \\[1em] \Rightarrow r = \sqrt{100} \\[1em] \Rightarrow r = 10 \text{ cm}.$

Total surface area of hemisphere = 3πr².

Putting values we get,

Total surface area of hemisphere = $3 \times 3.14 \times (10)^2$

$= 3 \times 3.14 \times 100 \\[1em] = 942 \text{ cm}^2.$

Volume of hemisphere = $\dfrac{2}{3}πr^3$.

Volume of hemisphere = $\dfrac{2}{3} \times 3.14 \times 10^3$

$= \dfrac{2}{3} \times 3.14 \times 1000 \\[1em] = \dfrac{6280}{3} \\[1em] = 2093\dfrac{1}{3} \text{cm}^3.$

Hence, the surface area of hemisphere = 942 cm² and volume of hemisphere = $2093\dfrac{1}{3}\text{ cm}^3.$