Question

the height of a cylinder is twice the radius of its base. what expression represents the volume of the cylinder, in cubic units? 4πx² 2πx³ πx² + 2x 2 + πx³

Explanation:

Step1: Recall the formula for the volume of a cylinder

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

Step2: Identify the values of \(r\) and \(h\)

Given that \(r = x\) and \(h=2x\).

Step3: Substitute \(r\) and \(h\) into the formula

Substitute \(r = x\) and \(h = 2x\) into \(V=\pi r^{2}h\). We get \(V=\pi(x)^{2}(2x)\).

Step4: Simplify the expression

Using the rule of exponents \(a^{m}\times a^{n}=a^{m + n}\), \(V = 2\pi x^{2+1}=2\pi x^{3}\).

Answer:

\(2\pi x^{3}\) (the second option)