Question

what is the volume of this cylinder? round your answer to the nearest hundredth. 26 mm 13 mm cubic millimeters submit

Explanation:

Step1: Find the radius of the cylinder

The diameter of the cylinder is given as 26 mm. The radius \( r \) is half of the diameter, so \( r=\frac{26}{2} = 13 \) mm.

Step2: Recall the formula for the volume of a cylinder

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

Step3: Substitute the values of \( r \) and \( h \) into the formula

We know that \( r = 13 \) mm and \( h=13 \) mm. Substituting these values into the formula, we get:
\( V=\pi\times(13)^{2}\times13 \)
First, calculate \( 13^{2}=169 \), then \( 169\times13 = 2197 \). So \( V=\pi\times2197\approx3.14159\times2197\approx7209.66 \) (rounded to the nearest hundredth)

Answer:

\( 7209.66 \)