Question

Ratio of curved surface area of two hemispheres is 4:9,then the ratio of theri volumes:
A)16:81
B)64:729
C)8:27
D)2:3​

Answer 1

Answer:

the correct answer is (C)

Answer 2

Given:-

• Ratio of curved surface area of two hemispheres is 4:9.

To find:-

• Ratio of their volumes.

Solution:-

• Let radius of one sphere be r and ratio of bigger sphere be R.
• Curved surface area of sphere= 4πr²
• ∴ we are given that, $\frac{4\pi r^2 }{4\pi R^2 }$ = $\frac{4}{9}$  
• Hence, $\frac{r^2}{R^2} = \frac{4}{9}$  .
• Taking roots on both sides, $\frac{r}{R} =\frac{2}{3}$  
• Volume of sphere = $\frac{4\pi r^3 }{3}$  
• Ratio of volumes will be, $\frac{\frac{4 \pi r^3}{3} }{\frac{4 \pi R^3}{3} }$  
• On simplifying we get, $\frac{r^3}{R^3} = (\frac{2^3}{3^3} ) = \frac{8}{27} .$

Answer:-

∴ Ratio of volume of spheres = 8/27