Question

A cylindrical can of soup has a diameter of 7 cm and a height of 10 cm. How much soup is in the can, in terms of π?
Responses
A 61.25π
61.25π cm 3
B 122.5π
122.5π cm 3
C 245π
245π cm 3
D 490π

Answer 1

To find the volume of a cylindrical can of soup, we can use the formula for the volume of a cylinder:

\[
V = \pi r^2 h
\]

where:
- \( V \) is the volume,
- \( r \) is the radius of the base,
- \( h \) is the height.

Given that the diameter of the can is 7 cm, we can find the radius \( r \):

\[
r = \frac{\text{diameter}}{2} = \frac{7 \, \text{cm}}{2} = 3.5 \, \text{cm}
\]

The height \( h \) of the can is given as 10 cm.

Now we can plug the values of \( r \) and \( h \) into the volume formula:

\[
V = \pi (3.5)^2 (10)
\]

Calculating \( (3.5)^2 \):

\[
(3.5)^2 = 12.25
\]

Now substituting this back into the volume formula:

\[
V = \pi (12.25)(10) = 122.5\pi
\]

Thus, the volume of the soup in the can is \( 122.5\pi \, \text{cm}^3 \).

So the correct answer is:

**B 122.5π cm³**