A solid sphere has a radius 8 cm. It is melted to form a cube, 20% is lost in this process. The cube is further melted to form a cone and 20% is again lost in the process. What is the radius (in cm) of cone?
Answer & explanation
Correct answer: option 2
Radius of sphere = R
Radius of cone = r
Volume of Sphere = \(\frac{4}{3}\) \(\pi \)R3
(Volume of cube is 80% of sphere (since 20% is lost))
Volume of cube = \(\frac{4}{5}\) × \(\frac{4}{3}\) \(\pi \)R3
And volume of cone is further 80% of this; i.e.
volume of cone = \(\frac{4}{5}\) × \(\frac{4}{5}\) × \(\frac{4}{3}\) \(\pi \)R3
⇒ \(\frac{1}{3}\) \(\pi \)r3 = \(\frac{4}{3}\) × \(\frac{4}{5}\) × \(\frac{4}{5}\) \(\pi \)R3
⇒ r3 = \(\frac{(4)^3 R^3}{5^2}\)
⇒ r = \(\frac{4R}{\sqrt[3]{25}}\) = \(\frac{32}{\sqrt[3]{25}}\) cm