A hemisphere of lead of radius 6 cm is cast into a right circular cone of height 75 cm. The radius of the… · ABC26GN5053
Subject: General Aptitude · Chapter: Volume and Surface Area
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
Answer
Explanation
Let the radius of the cone be $R$ cm. Then, $\frac{1}{3} \pi \times R^{2} \times 75=\frac{2}{3} \pi \times 6 \times 6 \times 6$ $$\Leftrightarrow R^{2}=\left(\frac{2 \times 6 \times 6 \times 6}{75}\right)=\left(\frac{144}{25}\right)=\left(\frac{12}{5}\right)^{2} \Leftrightarrow R=\frac{12}{5} \mathrm{cm}=2.4 \mathrm{cm} .$$
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