Question

q. mike has a large plastic cup that he is going to fill with water. the plastic cup is in the shape of a cone as shown. which is closest to the volume of mike’s cup?

Explanation:

Step1: Recall the formula for the volume of a cone

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

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

From the diagram, the radius \( r = 3 \) inches and the height \( h=7 \) inches.

Step3: Substitute the values into the formula

Substitute \( r = 3 \) and \( h = 7 \) into the formula:
\[

$$\begin{align*} V&=\frac{1}{3}\times\pi\times(3)^{2}\times7\\ &=\frac{1}{3}\times\pi\times9\times7\\ & = 3\times\pi\times7\\ &=21\pi \end{align*}$$

\]
Using \( \pi\approx3.14 \), we get \( V\approx21\times3.14 = 65.94 \) cubic inches.

Answer:

The volume of Mike's cup is approximately \( 66 \) cubic inches (or \( 21\pi\approx65.94 \) cubic inches).