Question

15.Can someone help me?​

Answer 1

Answer:

The radius, in inches, of the base of the cone will be:

r = 6 inches

Hence, option B is correct.

Step-by-step explanation:

Given

The Volume of a right circular cone V = 24 π cubic inches

The height of the cone h = 2 inches

To determine

The radius of the base of the cone r = ?

Using the formula involving Volume m, height h, and radius r of a right circular cone.

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

substituting V = 24 π, h = 2 to find the radius r

$\left(24\pi \right)=\frac{1}{3}\left(2\right)\:\pi \:r^2$

switch sides

$\frac{1}{3}\left(2\right)\pi r^2=\left(24\pi \right)$

$\frac{1}{3}2\pi r^2=24\pi$

simplify

$2\pi r^2=72\pi$

Divide both sides by 2π

$\frac{2\pi r^2}{2\pi }=\frac{72\pi }{2\pi }$

$r^2=36$

$\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}$

$r=\sqrt{36},\:r=-\sqrt{36}$

Thus,

$r=6,\:r=-6$

As we know that the radius can not be negative.

Therefore, the radius, in inches, of the base of the cone will be:

• r = 6 inches

Hence, option B is correct.