A solid right cylinder having a base of diameter 10 cm and height 2 cm is melted and recast into right cylindrical coins with a base diameter of 1 cm and a 0.2 cm thickness. Find the number of coins that can be made.

Correct option is A

Given:

Diameter of base of cylinder= 10cm

Height of cylinder = 2cm

Diameter of coins = 1cm

Thickness of coin = 0.2cm

Formula Used:

Volume of cylinder $$= \pi r^2 h$$​​

Solution:

When cylinder is recast into coins then the volume remains constant

Hence

Volume of cylinder = n $$\times$$​ Volume of coins

Radius of cylinder =$$\frac{10}{2}$$​ =5 cm

Radius of coins =$$\frac{1}{2}$$​= 0.5cm

Thickness of coins =0.2cm

Now

​$$\pi (5)^2 (2) = n \times \pi (0.5)^2 (0.2)$$​​

​$$n= \frac{50}{0.25 \times 0.2} = 1000$$​​