Question

if the radius of a cone is 3 and the height is 7, what is its volume?
o a. 10π cm³
o b. 21π cm³
o c. 14π cm³
o d. 12π cm³

if a cone has a height of 9 cm and a radius of 3 cm, its volume is closest to:
o a 60 cm³
o b 84.78 cm³
o c 120 cm³
o d 90 cm³

Explanation:

Step1: Recall the volume formula for a cone

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

Step2: Solve the first problem

Given \(r = 3\) and \(h=7\). Substitute into the formula:
\(V=\frac{1}{3}\pi\times3^{2}\times7=\frac{1}{3}\pi\times9\times7 = 21\pi\mathrm{cm}^{3}\).

Step3: Solve the second problem

Given \(r = 3\) and \(h = 9\). Substitute into the formula:
\(V=\frac{1}{3}\pi\times3^{2}\times9=\frac{1}{3}\pi\times9\times9= 84.78\mathrm{cm}^{3}\) (using \(\pi\approx3.14\)).

Answer:

First problem: B. \(21\pi\mathrm{cm}^{3}\)
Second problem: B. \(84.78\mathrm{cm}^{3}\)