Question

lesson: formulating and interpreting volume of cones using e... a cone has a radius of 6 cm and a volume of 72πcm³. what is the height of the cone? a. 4 cm b. 8 cm c. 2 cm d. 6 cm to find the volume of a cone, you need to know: a. the radius of the base and the height b. the slant height and the radius c. the circumference and the height d. the diameter and the height

Explanation:

Step1: Recall the volume formula of a cone

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

Step2: Substitute the given values into the formula

We know that \(V = 72\pi\) \(cm^{3}\) and \(r=6\) \(cm\). Substituting these into the formula \(V=\frac{1}{3}\pi r^{2}h\), we get \(72\pi=\frac{1}{3}\pi\times6^{2}\times h\).

Step3: Simplify the equation

First, simplify \(\frac{1}{3}\pi\times6^{2}\times h\). \(\frac{1}{3}\times36\pi\times h = 12\pi h\). So the equation becomes \(72\pi=12\pi h\).

Step4: Solve for \(h\)

Divide both sides of the equation \(72\pi = 12\pi h\) by \(12\pi\). \(\frac{72\pi}{12\pi}=h\), which simplifies to \(h = 6\) \(cm\).

For the second question:

The volume formula of a cone \(V=\frac{1}{3}\pi r^{2}h\) directly shows that to calculate the volume, we need the radius of the base (\(r\)) and the height (\(h\)).

Answer:

First question: d. \(6\) \(cm\)
Second question: a. the radius of the base and the height