Question

radius of a cylinder is 6 inches and the height is 13 inches. find the exact volume of a cylinder.

Explanation:

Step1: Recall the formula for the volume of a cylinder

The formula for the volume \( V \) of a cylinder is \( V=\pi r^{2}h \), where \( r \) is the radius and \( h \) is the height.

Step2: Substitute the given values

Given that \( r = 6 \) inches and \( h=13 \) inches. Substitute these values into the formula:
\( V=\pi\times(6)^{2}\times13 \)

Step3: Calculate \( 6^{2} \)

First, calculate \( 6^{2}=36 \). So the formula becomes \( V = \pi\times36\times13 \)

Step4: Multiply 36 and 13

Calculate \( 36\times13 = 468 \). So the volume is \( V = 468\pi \) cubic inches. If we use \( \pi\approx3.14 \), then \( V=468\times3.14 = 1470.272 \approx1470.27 \) (matching the blue option's value, likely a typo in the image as 1470.27 is close to 1470.27).

Answer:

The volume of the cylinder is \( 468\pi \) cubic inches (or approximately \( 1470.27 \) cubic inches). If we consider the given options, the answer is 1470.27 (the blue - colored option with value 1470.27).