Question

35. If the base radius of a circular cone increases
by 30% and its height decreases by 20%, find
the percentage change in its volume.
A. Decreases by 10%
B. Increases by 4%
C. Increases by 10%
D. Increases by 35.2%​

Answer 1

Answer:

D. Increases by 35.2%​

Step-by-step explanation:

Let the initial radius and height be r and h respectively.

So, the volume (V) is:

$V = \frac{1}{3}\pi r^2h$

When radius increases by 30%.

$R =r + 30\% * r$

$R =r + 0.30 * r = r +0.3r = 1.3r$

When height decreases by 20%.

$H = h - 20\% * h$

$H = h - 0.20 * h = h - 0.20h = 0.8h$

So, the new volume V2 is:

$V_2 = \frac{1}{3}\pi R^2H$

This gives:

$V_2 = \frac{1}{3}\pi (1.3r)^2*(0.8h)$

$V_2 = \frac{1}{3}\pi *1.69r^2*0.8h$

Rewrite as:

$V_2 = \frac{1}{3}\pi *r^2h*1.69 * 0.8$

$V_2 = \frac{1}{3}\pi *r^2h*1.352$

Rewrite as:

$V_2 = \frac{1}{3}\pi *r^2h*(1 + 0.352)$

Express as percentage:

$V_2 = \frac{1}{3}\pi *r^2h*(1 + 35.2\%)$

This implies that the volume increases by 35.2%