Question
The length is 5 cm and the width is 3 cm. Find the volume of the cylinder, in cubic centimeters. Use 3.14 for pi. Round your answer to the nearest tenth.
Answers
GPT-4o mini
To find the volume of a cylinder, you can use the formula:
\[
V = \pi r^2 h
\]
where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.
In your case, you’ve provided dimensions where the length (5 cm) and width (3 cm) appear to suggest a rectangular base rather than a circular one. However, for a cylinder, you would typically need the radius.
If we assume that the width (3 cm) is the diameter of the circular base of the cylinder, then the radius \( r \) would be half of that:
\[
r = \frac{\text{diameter}}{2} = \frac{3 \, \text{cm}}{2} = 1.5 \, \text{cm}
\]
Given the height \( h \) as the length (5 cm), we can now substitute the values into the volume formula:
\[
V = \pi r^2 h = 3.14 \times (1.5 \, \text{cm})^2 \times 5 \, \text{cm
\]
Calculating \( (1.5)^2 \):
\[
(1.5)^2 = 2.25
\]
Now plug this back into the volume formula:
\[
V = 3.14 \times 2.25 \times 5
\]
Calculating \( 3.14 \times 2.25 \):
\[
3.14 \times 2.25 = 7.065
\]
Now, multiply this by the height (5 cm):
\[
V = 7.065 \times 5 = 35.325 \, \text{cm}^3
\]
Finally, rounding to the nearest tenth:
\[
V \approx 35.3 \, \text{cm}^3
\]
Therefore, the volume of the cylinder is approximately **35.3 cubic centimeters**.
\[
V = \pi r^2 h
\]
where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.
In your case, you’ve provided dimensions where the length (5 cm) and width (3 cm) appear to suggest a rectangular base rather than a circular one. However, for a cylinder, you would typically need the radius.
If we assume that the width (3 cm) is the diameter of the circular base of the cylinder, then the radius \( r \) would be half of that:
\[
r = \frac{\text{diameter}}{2} = \frac{3 \, \text{cm}}{2} = 1.5 \, \text{cm}
\]
Given the height \( h \) as the length (5 cm), we can now substitute the values into the volume formula:
\[
V = \pi r^2 h = 3.14 \times (1.5 \, \text{cm})^2 \times 5 \, \text{cm
\]
Calculating \( (1.5)^2 \):
\[
(1.5)^2 = 2.25
\]
Now plug this back into the volume formula:
\[
V = 3.14 \times 2.25 \times 5
\]
Calculating \( 3.14 \times 2.25 \):
\[
3.14 \times 2.25 = 7.065
\]
Now, multiply this by the height (5 cm):
\[
V = 7.065 \times 5 = 35.325 \, \text{cm}^3
\]
Finally, rounding to the nearest tenth:
\[
V \approx 35.3 \, \text{cm}^3
\]
Therefore, the volume of the cylinder is approximately **35.3 cubic centimeters**.