A sphere of diameter 12.6 cm is melted and cast into a right circular cone of height 25.2 cm.
Question:

A sphere of diameter 12.6 cm is melted and cast into a right circular cone of height 25.2 cm. The radius of the base of the cone is
(a) 6.3 cm
(b) 2.1 cm
(c) 6 cm
(d) 4 cm

Solution:

(a)  6.3 cm
Let cm be the radius of base of the cone.
Volume of the sphere = volume of the cone

$\Rightarrow \frac{4}{3} \pi \times(6.3)^{3}=\frac{1}{3} \pi \times r^{2} \times 25.2$

$\Rightarrow r^{2}=\frac{4 \times 6.3 \times 6.3 \times 6.3}{25.2}=39.69$

$\Rightarrow r=\sqrt{39.69}=6.3 \mathrm{~cm}$

 

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