The base radius and height of a right circular solid cone is 12 cm and 24 cm respectively. It is melted and recast into spheres of diameter 6 cm each. Find the numbers of spheres so formed.

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Solution

The correct option is C 32
Volume of the cone $= \frac{1}{3} π (12)^{2} \times 24 = 1152 π c m^{3}$
Radius of each spherical ball
$= \frac{6}{2} = 3 c m$
Volume of spherical ball
= $\frac{4}{3} π r^{3}$ = $\frac{4}{3} π (3)^{3}$
Number of spherical balls
$= \frac{3 \times 1152 π}{4 π (3)^{3}} = 32$

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The base radius and height of a right circular solid cone is 12 cm and 24 cm respectively. It is melted and recast into spheres of diameter 6 cm each. Find the numbers of spheres so formed.

The correct option is C 32Volume of the cone =13π(12)2×24=1152π cm3 Radius of each spherical ball =62=3cm Volume of spherical ball = 43πr3 = 43π(3)3 Number of spherical balls =3×1152π4π(3)3=32