High School

A food container is in the shape of a right circular cylinder.

To the nearest cubic inch, find the exact volume of the food container if the radius of the base measures 2.3 inches and the height of the container is 6.2 inches.

52 in³
76 in³
92 in³
103 in³

Answer :

To find the volume of a right circular cylinder, we use the formula:

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

Where:

  • [tex]V[/tex] is the volume of the cylinder.
  • [tex]r[/tex] is the radius of the base of the cylinder.
  • [tex]h[/tex] is the height of the cylinder.
  • [tex]\pi[/tex] is approximately 3.14159.

Given in the problem:

  • The radius [tex]r = 2.3[/tex] inches.
  • The height [tex]h = 6.2[/tex] inches.

Let's plug these values into the formula:

[tex]V = \pi (2.3)^2 (6.2)[/tex]

First, we calculate [tex](2.3)^2[/tex]:

[tex](2.3)^2 = 2.3 \times 2.3 = 5.29[/tex]

Now, we substitute this result back into the volume formula:

[tex]V = \pi \times 5.29 \times 6.2[/tex]

Next, let's calculate [tex]5.29 \times 6.2[/tex]:

[tex]5.29 \times 6.2 = 32.798[/tex]

Then, multiply this result by [tex]\pi[/tex]:

[tex]V = 3.14159 \times 32.798 \approx 103.020[/tex]

Rounding 103.020 to the nearest whole number gives us 103.

Therefore, the volume of the cylinder is approximately [tex]103 \text{ cubic inches}[/tex].

The correct answer is 103 in³.