Question

an oblique cone has a height equal to the diameter of the base. the volume of the cone is equal to 18π cubic units.
what is the radius of the cone?
2 units
3 units
6 units
9 units

Explanation:

Step1: Write the formula for the volume of a cone

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

Step2: Substitute \(r\) and \(h\) into the volume formula

Substitute \(r=x\) and \(h = 2x\) into \(V=\frac{1}{3}\pi r^{2}h\), we get \(V=\frac{1}{3}\pi x^{2}(2x)=\frac{2}{3}\pi x^{3}\).

Step3: Solve for \(x\)

Since \(V = 18\pi\), then \(\frac{2}{3}\pi x^{3}=18\pi\). Divide both sides by \(\pi\): \(\frac{2}{3}x^{3}=18\). Multiply both sides by \(\frac{3}{2}\): \(x^{3}=18\times\frac{3}{2}=27\). Take the cube - root of both sides: \(x = 3\).

Answer:

3 units