Question

A cylindrical vessel of height $10$ cm has base radius $60$ cm. If $d$ is the diameter of a spherical vessel of equal volume, then what is $d$ equal to?

• A. $30$ cm
• B. $60$ cm
• C. $90$ cm
• D. $120$ cm

Answer 1

Answer: (B)

$60$ cm

$r=60$ cm, $h=10$ cm
Volume of $B$ $=$ Volume of $A$
$\frac{4}{3}\pi {\left(\frac{d}{2}\right)}^3=\pi \times 60\times 60\times 10$
$\frac{4}{3}\times \pi \times \frac{1}{8}\times d^3=\pi \times 60\times 60\times 10$
$d^3=\frac{60\times 60\times 10\times 3\times 8}{4}$
$d^3=216000$
$\Rightarrow d=\sqrt[3]{3216\times 1000}=6\times 10=60$ cm