Question

Volume of a cone with height of 28 and diameter 10.5

Answer 1

To find the volume of a cone, you can use the formula:

\[
V = \frac{1}{3} \pi r^2 h
\]

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

Given that the diameter of the cone is 10.5, you can find the radius by dividing the diameter by 2:

\[
r = \frac{10.5}{2} = 5.25
\]

The height \( h \) of the cone is given as 28. Now, substitute the values of \( r \) and \( h \) into the volume formula:

\[
V = \frac{1}{3} \pi (5.25)^2 (28)
\]

First, calculate \( (5.25)^2 \):

\[
(5.25)^2 = 27.5625
\]

Now substitute this value back into the formula:

\[
V = \frac{1}{3} \pi (27.5625) (28)
\]

Now calculate \( 27.5625 \times 28 \):

\[
27.5625 \times 28 = 771.75
\]

Now substitute this into the volume formula:

\[
V = \frac{1}{3} \pi (771.75)
\]

Finally, multiply by \( \frac{1}{3} \) and use \( \pi \approx 3.14159 \):

\[
V \approx \frac{1}{3} \times 3.14159 \times 771.75 \approx 808.641
\]

Thus, the volume of the cone is approximately \( 808.64 \) cubic units.