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Volume and Surface Areas of Solids — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsVolume and Surface Areas of Solids2 Marks
Question
A solid metal cone with radius of base 12cm and height 24cm is melted to form solid spherical balls of diameter 6cm each. Find the number of balls thus formed.
✓

Answer

Radius of the cone = 12cm
Height of the cone = 24cm
Volume $=\frac{1}{3}\pi\text{r}^2\text{h}=\frac{1}{3}\pi\times12\times12\times24$
$=48\times24\times\pi\text{cm}^3$
Radius of each ball = 3cm
Volume of each ball $=-\frac{4}{3}\pi\text{r}^3=\frac{4}{3}\pi\times3\times3\times3=36\pi\text{cm}^3$
Total number of balls formed by melting the cone $=\frac{\text{volume of cone}}{\text{volume of a ball}}=\frac{48\times24\pi}{36\pi}=32$

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