Question

a cylinder has a radius of 7 cm and a height of 12 cm. what is its volume in terms of π?
a. 343πcm³
b. 294πcm³
c. 588πcm³
d. 420πcm³

Explanation:

Step1: Recall the formula for the volume of a cylinder

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

Step2: Substitute the given values into the formula

Given \(r = 7\mathrm{cm}\) and \(h=12\mathrm{cm}\), we substitute these into the formula: \(V=\pi\times(7)^{2}\times12\).

Step3: Calculate \(r^{2}\)

\((7)^{2}=7\times7 = 49\). So the formula becomes \(V=\pi\times49\times12\).

Step4: Calculate the product of the non - \(\pi\) terms

\(49\times12=(50 - 1)\times12=50\times12-1\times12=600 - 12=588\).

So the volume \(V = 588\pi\mathrm{cm}^3\).

Answer:

C. \(588\pi\mathrm{cm}^3\)