Question

1. what is the approximate volume of a cone with a radius of 7 cm and height of 15 cm?

a. 452.12 cm³
b. 601.44 cm³
c. 769.69 cm³
d. 1230.57 cm³

Explanation:

Step1: Recall the formula for the volume of a cone

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

Step2: Substitute the given values into the formula

Given \(r = 7\ \text{cm}\) and \(h=15\ \text{cm}\), we substitute into the formula: \(V=\frac{1}{3}\times\pi\times(7)^{2}\times15\).

Step3: Simplify the expression

First, calculate \((7)^{2}=49\). Then, \(\frac{1}{3}\times15 = 5\). So the formula becomes \(V = 5\times\pi\times49\).
\(V=245\pi\).

Step4: Calculate the numerical value

Taking \(\pi\approx3.1416\), we have \(V=245\times3.1416\).
\(V = 769.692\approx769.69\ \text{cm}^3\).

Answer:

C. \(769.69\ \text{cm}^3\)