Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: 2008 · Marks: · Difficulty:
A metallic sphere of radius 10.5 cm is melted and recast into small right circular cones, each of base radius 3.5 cm and height 3 cm . The number of cones so formed is
(a)105
(b)113
(c)126
(d)135
Answer
Answer (as printed): C
Explanation
Volume of sphere $$=\left[\frac{4}{3} \pi \times(10.5)^{3}\right] \mathrm{cm}^{3}=(4 \pi \times 10.5 \times 10.5 \times 3.5) \mathrm{cm}^{3} .$$ Volume of each cone $$\begin{aligned} & =\left[\frac{1}{3} \pi \times(3.5)^{2} \times 3\right] \mathrm{cm}^{3}=(\pi \times 3.5 \times 3.5) \mathrm{cm}^{3} . \\ & \therefore \text { Number of cones formed }=\frac{4 \pi \times 10.5 \times 10.5 \times 3.5}{\pi \times 3.5 \times 3.5}=126 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.