Question

A spherical iron ball of radius $9$ cm is melted and recast into three spherical balls. If the radii of two balls are $1$ cm and $8$ cm, find the radius of the third ball.

• A. $2cm$
• B. $3cm$
• C. $4cm$
• D. $6cm$

Answer 1

Answer: (D)

$6cm$

Let the radius of big ball $R=9$ cm

Let the radii of the three balls be $r_1,r_2,r_3$

where $r_1=1cm,r_2=8cm$

We know

Volume of iron ball $=$ Sum of volumes of $3$ balls

$\Rightarrow \frac{4}{3}\pi R^3=\frac{4}{3}\pi (r_1^3+r_2^3+r_3^3)$

$\Rightarrow {\left(9\right)}^3=1^3+8^3+r_3^3$

$\Rightarrow 729=1+512+r_3^3$

$\Rightarrow 216=r_3^3$

$r_3=\sqrt[3]{3216}=6$ cm

Therefore radius of third sphere is $6$ cm.