Question

Radius of a sphere formed by the combination of three spheres of radius 3 cm, 4 cm and 5 cm, is .

• A. 6 cm
• B. 12 cm
• C. 27 cm
• D. 64 cm

Answer 1

The correct option is A 6 cm

Let the radius of the larger sphere be R.
Given:
Radius of first sphere= $r_1=3cm$
Radius of second sphere = $r_2=4cm$
Radius of third sphere = $r_3=5cm$
We know that when we combine many solids to form one solid, the volume remains same.

$\Rightarrow$ Volume of the larger sphere = Sum of volume of three spheres
$\Rightarrow$ $\frac{4}{3}\pi R^3=\frac{4}{3}\pi {r_1}^3+\frac{4}{3}\pi {r_2}^3+\frac{4}{3}\pi {r_3}^3$
$\Rightarrow$ $R^3={r_1}^3+{r_2}^3+{r_3}^3$
$\Rightarrow$ $R^3=3^3+4^3+5^3$
$\Rightarrow$ $R^3=27+64+125$
$\Rightarrow$ $R^3=216$
$\Rightarrow$ $R^3=6^3$
$\Rightarrow$R = 6 cm

$\therefore$ Radius of the larger sphere is 6 cm.