Question
if a diameter of 16n and a height of 7 inches,what is the volume in cubic inches
round to the nearest hundredth and use 3.14 for pi
round to the nearest hundredth and use 3.14 for pi
Answers
GPT-4o mini
To calculate 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.
Given:
- Diameter = \( 16n \), which means the radius \( r = \frac{16n}{2} = 8n \).
- Height \( h = 7 \) inches.
- Using \( \pi \approx 3.14 \).
Now substitute these values into the volume formula:
\[
V = 3.14 \times (8n)^2 \times 7
\]
Calculating \( (8n)^2 \):
\[
(8n)^2 = 64n^2
\]
Now, substituting back into the volume formula:
\[
V = 3.14 \times 64n^2 \times 7
\]
Calculating \( 64n^2 \times 7 \):
\[
64n^2 \times 7 = 448n^2
\]
Now substitute this value into the formula:
\[
V = 3.14 \times 448n^2
\]
Now calculate \( 3.14 \times 448 \):
\[
3.14 \times 448 = 1407.92
\]
So, the expression for the volume is:
\[
V = 1407.92n^2
\]
Thus, the volume of the cylinder in cubic inches is \( 1407.92n^2 \). The final result depends on the value of \( n \); if \( n \) is given, you can multiply \( 1407.92 \) by the corresponding value of \( n^2 \) to find the specific volume.
\[
V = \pi r^2 h
\]
where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.
Given:
- Diameter = \( 16n \), which means the radius \( r = \frac{16n}{2} = 8n \).
- Height \( h = 7 \) inches.
- Using \( \pi \approx 3.14 \).
Now substitute these values into the volume formula:
\[
V = 3.14 \times (8n)^2 \times 7
\]
Calculating \( (8n)^2 \):
\[
(8n)^2 = 64n^2
\]
Now, substituting back into the volume formula:
\[
V = 3.14 \times 64n^2 \times 7
\]
Calculating \( 64n^2 \times 7 \):
\[
64n^2 \times 7 = 448n^2
\]
Now substitute this value into the formula:
\[
V = 3.14 \times 448n^2
\]
Now calculate \( 3.14 \times 448 \):
\[
3.14 \times 448 = 1407.92
\]
So, the expression for the volume is:
\[
V = 1407.92n^2
\]
Thus, the volume of the cylinder in cubic inches is \( 1407.92n^2 \). The final result depends on the value of \( n \); if \( n \) is given, you can multiply \( 1407.92 \) by the corresponding value of \( n^2 \) to find the specific volume.