Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: 2007 · Marks: · Difficulty:
Some solid metallic right circular cones, each with radius of the base 3 cm and height 4 cm, are melted to form a solid sphere of radius 6 cm . The number of right circular cones is
(a)6
(b)12
(c)24
(d)48
Answer
Answer (as printed): C
Explanation
Volume of sphere $=\left(\frac{4}{3} \pi \times 6^{3}\right) \mathrm{cm}^{3}=(288 \pi) \mathrm{cm}^{3}$. $$\begin{aligned} & \text { Volume of each cone }=\left(\frac{1}{3} \pi \times 3^{2} \times 4\right) \mathrm{cm}^{3}=(12 \pi) \mathrm{cm}^{3} . \\ & \therefore \text { Number of cones }=\frac{288 \pi}{12 \pi}=24 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.