Practice | Hashtable

1. A hemisphere of lead of radius 6 cm is cast into a right circular cone of height 75 cm. The radius of the base of the cone is :

A. 1.4 cm

B. 2 cm

C. 2.4 cm

D. 4.2 cm

Solution:

Let the radius of the cone be R cm
Then,

\begin{aligned} \frac{1}{3} π \times R^{2} \times 75 = \frac{2}{3} π \times 6 \times 6 \times 6 \\ \Rightarrow R^{2} = (\frac{2 \times 6 \times 6 \times 6}{75}) \\ \Rightarrow R^{2} = \frac{144}{25} \\ \Rightarrow R^{2} = \frac{{(12)}^{2}}{{(5)}^{2}} \\ \Rightarrow R = \frac{12}{5} \\ \Rightarrow R = 2.4 c m \end{aligned}

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