Question
Colin is purchasing a can of beans. The can is in the shape of a right circular cylinder. If the volume of the can is 31.79 inches3 , and the diameter is 3 inches, what is the height of the can? Use 3.14 for π and round to the nearest tenth.(1 point) inches
Answers
GPT-4o mini
To find the height of the cylindrical can of beans, 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, and \( h \) is the height.
Given that the diameter of the can is 3 inches, we can find the radius:
\[
r = \frac{diameter}{2} = \frac{3 \text{ inches}}{2} = 1.5 \text{ inches}
\]
Now we can replace \( V \) with 31.79 inches³ and \( r \) with 1.5 inches in the volume formula:
\[
31.79 = 3.14 \times (1.5)^2 \times h
\]
Calculating \( (1.5)^2 \):
\[
(1.5)^2 = 2.25
\]
Now substituting back into the equation:
\[
31.79 = 3.14 \times 2.25 \times h
\]
Calculating \( 3.14 \times 2.25 \):
\[
3.14 \times 2.25 = 7.065
\]
So we have:
\[
31.79 = 7.065 \times h
\]
To find \( h \), we can divide both sides by 7.065:
\[
h = \frac{31.79}{7.065} \approx 4.49
\]
Rounding to the nearest tenth, the height of the can is:
\[
\boxed{4.5} \text{ inches}
\]
\[
V = \pi r^2 h
\]
where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.
Given that the diameter of the can is 3 inches, we can find the radius:
\[
r = \frac{diameter}{2} = \frac{3 \text{ inches}}{2} = 1.5 \text{ inches}
\]
Now we can replace \( V \) with 31.79 inches³ and \( r \) with 1.5 inches in the volume formula:
\[
31.79 = 3.14 \times (1.5)^2 \times h
\]
Calculating \( (1.5)^2 \):
\[
(1.5)^2 = 2.25
\]
Now substituting back into the equation:
\[
31.79 = 3.14 \times 2.25 \times h
\]
Calculating \( 3.14 \times 2.25 \):
\[
3.14 \times 2.25 = 7.065
\]
So we have:
\[
31.79 = 7.065 \times h
\]
To find \( h \), we can divide both sides by 7.065:
\[
h = \frac{31.79}{7.065} \approx 4.49
\]
Rounding to the nearest tenth, the height of the can is:
\[
\boxed{4.5} \text{ inches}
\]