Question

what is the approximate volume of a cone with a radius of 7 cm and height of 15 cm? a. 1230.57 cm³ b. 452.12 cm³ c. 769.69 cm³ d. 601.44 cm³

Explanation:

Step1: Recall the formula for the volume of 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: Substitute the given values into the formula

Given \(r = 7\mathrm{cm}\) and \(h=15\mathrm{cm}\), substitute into \(V=\frac{1}{3}\pi r^{2}h\). So \(V=\frac{1}{3}\times\pi\times(7)^{2}\times15\).

Step3: Simplify the expression

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

Step4: Calculate the numerical value

Taking \(\pi\approx3.14\), then \(V=245\times3.14=769.3\approx769.69\mathrm{cm}^3\) (due to possible rounding differences in intermediate steps in some calculators for more precise \(\pi\) values).

Answer:

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