Question

a cylinder is shown below.
(image of a cylinder with r = 8 and h = 10)
fill in the boxes to complete the equation and find the volume in terms of π.
□(□)²□ = □ cubic units

Explanation:

Step1: Recall the volume formula for 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.

Step2: Identify the values of \( r \) and \( h \)

From the diagram, the radius \( r = 8 \) and the height \( h=10 \).

Step3: Substitute the values into the formula

Substitute \( r = 8 \) and \( h = 10 \) into the formula \( V=\pi r^{2}h \). So we have \( V=\pi\times(8)^{2}\times10 \).

Step4: Calculate \( (8)^{2}\times10 \)

First, calculate \( 8^{2}=64 \), then multiply by 10: \( 64\times10 = 640 \). So the volume \( V = 640\pi \). So the equation is \( \pi\times(8)^{2}\times10=640\pi \).

Answer:

\(\pi\times(8)^{2}\times10 = 640\) (So the boxes are filled with \(\pi\), \(8\), \(\times10\), and \(640\pi\) respectively. But following the format of the equation in the problem, the filled equation is \(\pi(8)^{2}10 = 640\pi\) and the volume is \(640\pi\) cubic units.)