25. if a cone has a volume of 300π cm³ and a height of 15 cm, what is the radius of the base?\na. 6 cm\nb. 7…

Explanation:

Step1: Recall the volume formula of a cone

The volume formula of a cone is (V=\frac{1}{3}\pi r^{2}h), where (V) is the volume, (r) is the radius of the base, and (h) is the height.

Step2: Substitute the given values into the formula

We are given that (V = 300\pi\space cm^{3}) and (h=15\space cm). Substituting these into the formula (V=\frac{1}{3}\pi r^{2}h), we get (300\pi=\frac{1}{3}\pi r^{2}\times15).

Step3: Simplify the equation

First, cancel out (\pi) from both sides of the equation. The equation becomes (300=\frac{1}{3}\times15\times r^{2}). Then, (\frac{1}{3}\times15 = 5), so the equation is (300 = 5r^{2}).

Step4: Solve for (r^{2})

Divide both sides of the equation (300 = 5r^{2}) by (5). We have (r^{2}=\frac{300}{5}=60).

Step5: Solve for (r)

Take the square root of both sides. (r=\sqrt{60}). Simplify (\sqrt{60}=\sqrt{4\times15}=2\sqrt{15}\space cm).

Answer:

d. (2\sqrt{15}\space cm)