Question

examine the cone.
answer the questions about the cone.
what is the base area?
what is the volume?

Explanation:

Step1: Calculate the base area

The base of a cone is a circle. The formula for the area of a circle is \(A = \pi r^{2}\). Given the radius \(r = 4\) in (since the diameter is not given and we assume the 4 in is the radius - if it were diameter, radius would be 2 in. But standard notation in such problems, if only one linear measure for circular base is given as a single number without 'diameter' label, we take it as radius).

$$A=\pi\times4^{2}=16\pi$$

Step2: Calculate the volume

The formula for the volume of a cone is \(V=\frac{1}{3}Ah\) (where \(A\) is the base area and \(h\) is the height). We know \(A = 16\pi\) and \(h=5.5\) in.

$$V=\frac{1}{3}\times16\pi\times5.5=\frac{88}{3}\pi$$

Answer:

The base area is \(16\pi\) in² and the volume is \(\frac{88}{3}\pi\) in³.