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

D. Increases by 35.2%​

Explanation:

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

So, the volume (V) is:

`V = (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 = (1)/(3)\pi R^2H`

This gives:

`V_2 = (1)/(3)\pi (1.3r)^2*(0.8h)`

`V_2 = (1)/(3)\pi *1.69r^2*0.8h`

Rewrite as:

`V_2 = (1)/(3)\pi *r^2h*1.69 * 0.8`

`V_2 = (1)/(3)\pi *r^2h*1.352`

Rewrite as:

`V_2 = (1)/(3)\pi *r^2h*(1 + 0.352)`

Express as percentage:

`V_2 = (1)/(3)\pi *r^2h*(1 + 35.2\%)`

This implies that the volume increases by 35.2%