Question

Choose the correct answer from the alternatives given.
The radius of a metallic cylinder is 3 cm and its height is 5 cm. It is melted and moulded into small cones, each of height 1 cm and base radius 1 mm. The number of such cones formed, is

• A. 450
• B. 1,350
• C. 8,500
• D. 13,500

Answer 1

Answer: (D)

13,500

Volume of cylinder
= $\pi r^{2}h=\pi \times 9\times 5=45\pi c{m}^3$
Volume of a cone = $\frac{1}{3}\pi r^{2}h$
= $\frac{1}{3}\times \pi \times \frac{1}{100}\times 1=\frac{\pi }{300}c{m}^3$
According to the question,
Number of cones $\times$ Volume of a cone = Volume of cylinder
$\therefore$ Number of cones= $\frac{45\pi }{\pi /300}=45\times$ $300=13500$