Question
A solid sphere of radius $15\ cm$ is melted and recast into solid right circular cones of radius $2.5\ cm$ and height $8\ cm.$ Calculate the number of cones recast.
✓
Answer
Radius of a solid sphere $= R = 15\ cm$
$\therefore$ Volume of sphere melted = $\frac{4}{3} \pi R ^3=\frac{4}{3} \times \pi \times 15 \times 15 \times 15$
Radius of each cone recasted $= r = 2.5\ cm$
Height of each cone recasted $= h = 8\ cm$
$\therefore$ Volume of each one cone recasted $= \frac{1}{3} \pi r ^2 h =\frac{1}{3} \times \pi \times 2.5 \times 2.5 \times 8$
$\therefore$ Number of cones recasted $=\frac{\text { Volume of sphre melted }}{\text { Volume of each cone formed }}$
$=\frac{\frac{4}{3} \times \pi \times 15 \times 15}{\frac{1}{3} \times \pi \times 2.5 \times 2.5 \times 8}$
$=270$
$\therefore$ Volume of sphere melted = $\frac{4}{3} \pi R ^3=\frac{4}{3} \times \pi \times 15 \times 15 \times 15$
Radius of each cone recasted $= r = 2.5\ cm$
Height of each cone recasted $= h = 8\ cm$
$\therefore$ Volume of each one cone recasted $= \frac{1}{3} \pi r ^2 h =\frac{1}{3} \times \pi \times 2.5 \times 2.5 \times 8$
$\therefore$ Number of cones recasted $=\frac{\text { Volume of sphre melted }}{\text { Volume of each cone formed }}$
$=\frac{\frac{4}{3} \times \pi \times 15 \times 15}{\frac{1}{3} \times \pi \times 2.5 \times 2.5 \times 8}$
$=270$
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