A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recast into a sphere.

Question:

A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recast into a sphere. The radius of the sphere is
(a) 4.2 cm
(b) 2.1 cm
(c) 2.4 cm
(d) 1.6 cm

Solution:

(b) 2.1 cm

Let r cm be the radius of the sphere.
Volume of the cone = volume of the sphere

$\Rightarrow \frac{1}{3} \pi \times 2.1 \times 2.1 \times 8.4=\frac{4}{3} \pi r^{3}$

$\Rightarrow r^{3}=2.1 \times 2.1 \times 2.1$

$\Rightarrow r=2.1 \mathrm{~cm}$

 

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