Find the volume, in cubic inches, of a cylinder with a diameter of 16 inches and a height of 7 inches. Round your answer to the nearest hundredth. (1 point) cubic inches
To find the volume of a cylinder, you can use the formula:
\[ V = \pi r^2 h \]
where \( V \) is the volume of the cylinder, \( \pi \) is a constant (approximately 3.14159), \( r \) is the radius of the base of the cylinder, and \( h \) is the height of the cylinder.
In your case, the diameter of the cylinder is given as 16 inches, so the radius \( r \) is half of the diameter:
\[ r = \frac{diameter}{2} = \frac{16\ inches}{2} = 8\ inches \]
The height \( h \) of the cylinder is given as 7 inches.
Let's plug these values into the formula:
\[ V = \pi (8\ inches)^2 (7\ inches) \]
\[ V = \pi (64\ inches^2) (7\ inches) \]
\[ V = 448\ \pi\ inches^3 \]
Using the value of \( \pi \) as approximately 3.14159 (you can use the \( \pi \) button on a calculator for a more accurate value):
\[ V \approx 448 \times 3.14159\ inches^3 \]
\[ V \approx 1407.24512\ inches^3 \]
Rounded to the nearest hundredth, the volume of the cylinder is:
\[ V \approx 1407.25\ cubic\ inches \]