Question

A metallic sphere of radius 10.5 cm is melted and then recast into smaller cones, each of radius 3.5 cm and height 3 cm, How many cones are obtained?

Answer 1

Volume of sphere = $\frac{4}{3}$$\pi$$r^3$
= $\frac{4}{3}$ $\times$ $\frac{22}{7}$ $10.5\times 10.5\times 10.5$
Volume of metallic sphere = 4851 cm³
Now,
Volume of one cone = $\frac{1}{3}$$\pi$$r^2$h
= $\frac{4}{3}$ $\times$$\frac{22}{7}$ $3.5\times 3.5\times 3$
Volume of one cone = 38.5 cm³
Total number of cones = Volume of metallic sphere/volume of one cone
= $\left(\frac{4851}{38.5}\right)$
= 126 cones
Total number of cones can be formed is 126