Question

A solid metallic sphere of diameter 21 cm is melted and recast into a number of smaller cones, of diameter 3.5 cm and height 3cm. The number of cones so formed is:

• A. 405
• B. 540
• C. 504
• D. 254

Answer 1

The correct option is C 504

Radius of the sphere$=\frac{21}{2}cm$
Volume of the sphere$=\frac{4}{3}\pi (\frac{21}{2}{)}^{3}c{m}^3$
Radius of the cone$=\frac{7}{4}cm$ and height$=3cm$
Volume of cone$=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\pi (\frac{7}{4}{)}^2\times 3c{m}^3$
Let the number of cones formed be $n$. Then, $n\times \frac{1}{3}\pi \times (\frac{7}{4}{)}^2\times 3=\frac{4}{3}\pi \times (\frac{21}{2}{)}^3\to n=504$.