Question

the ratio of surface area of sphere and curved surface area of a hemisphere is 9 : 2.
find ratio of their volume. ​

Answer 1

Surface area of sphere=4πR²

Curved surface area of a hemisphere = 2πr²

According to the question

4πR²/ 2πr²= 9/2

2R²/r² = 9/2

R²/r²=9/4

R/r= 3/2

$Volume \: of \: sphere = \frac{4}{3} \pi \: R ^{3} \\ </p><p>Volume \: of \: hemisphere = \frac{2}{3} \pi \: r^{3} \\ Ratio \: of \:their\: volume = \frac{ \frac{4}{3} \pi \: (3) ^{3} }{ \frac{2}{3}\pi ({2} )^{3} } \: \: \: \: \\ \: \: \: \: \: \: \: \: \: \: = \frac{ \frac{4}{3} \times 27}{ \frac{2}{3} \times 8} \\ \: \: \: \: \: \: \: \: \: \: = \frac{36}{ \frac{16}{3} } \\ \: \: \: \: \: \: \: \: \: = 36 \times \frac{3}{16} \\ \: \: \: \: \: \: \: \: \: = \frac{27}{4}$

Therefore, Ratio of their volume = 27:4