Question

1. what is the volume of soup that will fit in a cylindrical - shaped can with a height that is 2 inches longer than the radius?

○ ( v = pi r^2 + 2pi r )
○ ( v = pi^3 r^3 + 8pi^3 r^2 )
○ ( v = pi r^3 + 2pi r^2 )
○ ( v = pi^3 r + 2pi^2 r )

Explanation:

Step1: Recall the formula for the volume of a cylinder

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

Step2: Determine the height in terms of the radius

We are given that the height \( h \) is 2 inches longer than the radius \( r \). So, \( h = r + 2 \).

Step3: Substitute the height into the volume formula

Substitute \( h=r + 2 \) into the volume formula \( V=\pi r^{2}h \). We get:
\[

$$\begin{align*} V&=\pi r^{2}(r + 2)\\ &=\pi r^{2}\times r+\pi r^{2}\times2\\ &=\pi r^{3}+2\pi r^{2} \end{align*}$$

\]

Answer:

\( V = \pi r^{3}+2\pi r^{2} \) (the third option)