Question

10
a right circular cone has a volume of 2,700π cubic centimeters and
the area of its base is 225π square centimeters. what is the slant
height, in centimeters, of this cone?
a 12
b 15
c 36
d 39

Explanation:

Step1: Find radius from base area

Base area $A = \pi r^2 = 225\pi \implies r^2 = 225 \implies r = 15$ cm

Step2: Find height using volume formula

Volume $V = \frac{1}{3}\pi r^2 h = 2700\pi$. Substitute $r^2=225$: $\frac{1}{3}\times225h = 2700 \implies 75h=2700 \implies h=36$ cm

Step3: Calculate slant height

Slant height $l = \sqrt{r^2 + h^2} = \sqrt{15^2 + 36^2} = \sqrt{225 + 1296} = \sqrt{1521} = 39$ cm

Answer:

D. 39