Answer: C
Let the radius of the cone be \(r\) cm. \(\therefore \cfrac{1}{3}\pi r^2 \times 42 = \cfrac{4}{3}\pi (8)^3 + \cfrac{4}{3}\pi (10)^3\) Or, \(42r^2 = 4(8^3 + 10^3)\) Or, \(42r^2 = 4 \times (512 + 1000)\) Or, \(r^2 = \cfrac{4 \times 1512}{42}\) Or, \(r^2 = 144\) Or, \(r = 12\) \(\therefore\) The radius of the cone is 12 cm.
Let the radius of the cone be \(r\) cm. \(\therefore \cfrac{1}{3}\pi r^2 \times 42 = \cfrac{4}{3}\pi (8)^3 + \cfrac{4}{3}\pi (10)^3\) Or, \(42r^2 = 4(8^3 + 10^3)\) Or, \(42r^2 = 4 \times (512 + 1000)\) Or, \(r^2 = \cfrac{4 \times 1512}{42}\) Or, \(r^2 = 144\) Or, \(r = 12\) \(\therefore\) The radius of the cone is 12 cm.