If the radius of the base of a right circular cylinder is decreased by 24% and its height isincreased by 262%, then what is the percentage increase (closest integer) in itsvolume?

Correct option is B

Given:

The radius of the base of the right circular cylinder is decreased by 24%, so the new radius becomes 76% of the original radius.

The height of the cylinder is increased by 262%, so the new height becomes 362% of the original height.

We need to find the percentage increase in the volume of the cylinder.

Formula Used: 

The volume V of a right circular cylinder is given by the formula:

Volume of cylinder = πr ²h

where:

r is the radius of the base,

h is the height of the cylinder.

Solution:

​$$V_{\text{new}} = \pi \left(0.76r\right)^2 \times \left(3.62h\right)$$​​

Now, 

$$\frac{V_{\text{new}}}{V_{\text{original}}} = \frac{\pi \left(0.76r\right)^2 \times 3.62h}{\pi r^2 h}$$​​

​$$= \frac{(0.76)^2 \times 3.62}{1}$$​​

​$$= 0.5776 \times 3.62$$​​

= 2.091792

Percentage increase = (2.091792 − 1) × 100 = 1.091792 × 100 = 109.18%

Alternate Solution: ​

Radius = -24%(decrease)

Height = +262%(increase) 

Now , 

​$$-24-24+262+\frac{(-24)(-24)}{100}+\frac{(-24)(262)}{100}+\frac{(-24)(262)}{100}+\frac{(-24)(-24)(262)}{10000} \\ \ \\ = 214 +5.76-62.88-62.88+15.0912\\ \ \\ = 109.0912\%$$​​