Find the volume of the cylinder.
Height = 6 cm
Radius = 3 cm
Slant height = 8 cm
(1 point)
169.56 cubic centimeters
678.24 cubic centimeters
339.12 cubic centimeters
226.08 cubic centimeters
To find the volume of a cylinder, we use the formula:
\[ V = \pi r^2 h \]
where \( V \) is the volume, \( r \) is the radius of the base of the cylinder, \( h \) is the height of the cylinder, and \( \pi \) is the mathematical constant approximately equal to 3.14159.
Given the radius \( r = 3 \) cm and the height \( h = 6 \) cm, we plug these values into the formula:
\[ V = \pi (3 \text{ cm})^2 (6 \text{ cm}) \]
\[ V = \pi (9 \text{ cm}^2) (6 \text{ cm}) \]
\[ V = 54\pi \text{ cm}^3 \]
Using the approximate value for \( \pi \), \( 3.14159 \), we get:
\[ V \approx 54 \times 3.14159 \text{ cm}^3 \]
\[ V \approx 169.64646 \text{ cm}^3 \]
Rounding to the nearest hundredth, as is typically the case with volume, we get:
\[ V \approx 169.65 \text{ cm}^3 \]
The closest answer from the provided options is 169.56 cubic centimeters, which might be due to rounding \( \pi \) to a different number of decimal places. However, since the difference is very small and likely due to a minor variation in the use of \( \pi \), 169.56 cubic centimeters would be the appropriate answer to select from your list.