Question

A sphere and a hemisphere have the same volume. What is the ratio of their radii?

Answer 1

Answer:

here is your answer. ✌ hope it helps you.

Step-by-step explanation:

Description for Correct answer:

Let the radius of hemisphere and sphere be 'r' and 'R'

⇒43πR3=23πr3

R3r3=12

Rr=12–√3

⇒ Ratio of curved sufrace area

=4πR22πr2=2R2r2=2×1(2–√3)2

=2(2)2/3⇒Rr=21/31

Answer 2

Let the radius of hemisphere and sphere be 'r' and 'R'

$\tt\purple⇒ \frac{4}{3}πR3 = \frac{2}{3}πr3$

$\tt\purple⇒ \frac{R3}{r3}=12$

$\tt\purple⇒ \frac{R}{r}=12– \sqrt{3}$

$\tt\purple⇒ Ratio \: of \: curved \: sufrace \: area$

$\tt\purple⇒ \frac{4πR2}{2πr2}^{2} = \frac{2R}{2r2}= \frac{2×1}{(2–√3)2}$

$\tt\purple⇒ \frac{2}{(2)2/3}$

$\tt\purple⇒ \frac{(2)2/3}{1}$