Question 44
A solid metal sphere has radius 14 cm. It is melted to form small cones of radius 1.75 cm and height 3.5 cm. How many small cones will be obtained from the sphere?
Solution
Volume of sphere = $$\frac{4}{3}\pi\ \times r^3=\frac{4}{3}\pi\ \times14^3=\frac{10976}{3}\pi\ \ .$$
Volume of each cone is = $$\frac{1}{3}\pi\times r^2\times h=\frac{1}{3}\pi\times1.75^2\times3.5=\frac{10.71875}{3}\pi\ \ .$$
So, required number = $$\frac{\frac{10976}{3}\pi\ }{\frac{10.71875}{3}\pi\ }=1024\ .$$
C is correct choice.
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