Q.A solid sphere has a surface area of 616 square cm. It is melted to form 14 identical right circular cones, each with a height of 2 cm. Find the diameter of the base of each cone.

Let the radius of the sphere be \(r\) cm. ∴ \(4\pi r^2 = 616\) ⇒ \(4 \times \cfrac{22}{7} \times r^2 = 616\) ⇒ \(r^2 = \cfrac{616 \times 7}{22 \times 4} = 49\) ⇒ \(r = 7\) ∴ Volume of the sphere = \(\cfrac{4}{3}\pi \times 7^3\) cubic cm Let the radius of the base of each cone be \(x\) cm. According to the question: \((\cfrac{1}{3}\pi x^2 \times 2) \times 14 = \cfrac{4}{3}\pi \times 7^3\) ⇒ \(\cfrac{28}{3}x^2 = \cfrac{4 \times 343}{3}\) ⇒ \(x^2 = \cfrac{1372}{28} = 49\) ⇒ \(x = 7\) ∴ Diameter of the base of each cone = \(7 \times 2 = 14\) cm.
Similar Questions