Question

Eight metallic spheres; each of radius 2 mm, are melted and cast into a single sphere. Calculate the radius of the new sphere.

• A. 9 mm
• B. 4 mm
• C. 1 mm
• D. 3 mm

Answer 1

The correct option is B

4 mm

Radius of 1 metallic sphere = 2 mm
$\text{Volume}=\frac{4}{3}\pi r^3$
$=\frac{4}{3}\times \frac{22}{7}\times 2\times 2\times 2=88\times \frac{8}{21}$

$\text{Volume of 8 spheres}=88\times 8\times \frac{8}{21}$

$\text{let the radius of new sphere}=y\text{Volume}=\frac{4}{3}\pi \times y^3$
$=\frac{4}{3}\times \frac{22}{7}\times y^3$
$=\frac{88}{21}\times y^3$

$\text{Volume of the new sphere}=\text{volume of the 8 old spheres}$

$\frac{88}{21}\times y^3=88\times 8\times \frac{8}{21}$
$y^3=88\times 8\times \frac{8}{21}\times \frac{21}{88}$
$y^3=64$
$y=\sqrt[3]{364}=4$
$y=4mm$