Question

The base diameter of a solid in the form of a cone is $6$ cm and the height of the cone is $10$ cm It is melted and recast into spherical balls of diameter $1$ cm. Find the number of balls, thus obtained

• A. $180$
• B. $120$
• C. $200$
• D. $160$

Answer 1

Answer: (A)

$180$

Let the number of spherical balls be n. Then, the volume of the cone will be equal to the sum of the volumes of the spherical balls. The radius of the base of the cone $=\frac{6}{2}cm=3cm$

and the radius of the sphere $=\frac{1}{2}cm$.

Now, the volume of the cone

$=\frac{1}{3}\pi \times 3^2\times 10c{m}^3=30\pi c{m}^2$

and the volume of each sphere

$=\frac{4}{3}\pi {\left(\frac{1}{2}\right)}^{3}c{m}^3=\frac{\pi }{6}c{m}^3$

Hence, we have

$n\frac{\pi }{6}=30\pi \Rightarrow n=6\times 30=180$

Hence, the required number of balls $=180$