Question

The radius and height of a solid cylinder are increased by 2% each. What will be the approximate percentage increase in volume?
A) 6.76 B) 5.88
C) 6.12 D) 3.34

Answer 1

Given :

A cylinder with radius 'r' and height 'h'

Increase in radius and height = 2%

To find :

percentage increase in volume.

Solution :

Volume of a cylinder = $\pi r^2h$

Radius of the cylinder after increase of 2% = r + (2% of r)

                                                                       = r + 0.02r

                                                                       = 1.02r

Similarly height of the cylinder after increase of 2% = 1.02h

New volume = $\pi (1.02r)^2(1.02h)$

                     = 1.0612(πr²h)

increase in volume = 1.0612(πr²h) - πr²h

                               = 0.0612(πr²h)

Now percentage increase in volume = $\frac{\text{increase in volume}}{\text{initial volume}} \times 100$

= $\frac{0.0612(\pi r^2h )}{\pi r^2h}\times 100$

= 0.0612 × 100

= 6.12%

Option C) 6.12 is the answer.