Question

The volumes of two spheres are in the ratio 27:64. Find their radii if the sum of their radii is 28 cm.

• A. $12cm,16cm$
• B. $18cm,17cm$
• C. $22cm,15cm$
• D. $16cm,22cm$

Answer 1

Answer: (A)

$12cm,16cm$

Volume of a sphere $=\frac{4}{3}\pi r^3$

Given, ratio of their volumes is: $V_1:V_2=27:64$
$\frac{4}{3}\pi {r_1}^3:\frac{4}{3}\pi {r_3}^{2}h=27:64$
${r_1}^3:{r_2}^3=27:64$
$=>r_1:r_2=3:4$
Let $>r_1=3a;r_2=4a$

Given, $r_1+r_2=28$

$=>3a+4a=28$

$7a=28$

$a=4$

$3a=12cm;4a=16cm$