Question

a cylinder is shown below
r = 8
h = 6
fill in the boxes to complete the equation and find the volume in terms of π.
□((□)²□) = □ cubic units

Explanation:

Step1: Recall cylinder volume formula

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

From the diagram, \( r = 8 \) and \( h=6 \).

Step3: Substitute values into formula

Substitute \( r = 8 \) and \( h = 6 \) into the formula \( V=\pi r^{2}h \). So we have \( \pi\times(8)^{2}\times6 \).

Step4: Calculate the numerical part

First, calculate \( 8^{2}=64 \), then \( 64\times6 = 384 \). So the volume is \( \pi\times8^{2}\times6=384\pi \). Filling in the boxes: the first box is \( \pi \), the second is \( 8 \), the third is \( \times6 \) (or just \( 6 \) considering the order of operations in the formula structure), and the last box is \( 384\pi \). But following the box structure \( \square((\square)^{2}\square)=\square \), we put \( \pi \) in the first box, \( 8 \) in the second box, \( 6 \) (or \( \times6 \)) in the third box, and \( 384\pi \) in the last box. Calculating \( \pi\times(8)^{2}\times6=\pi\times64\times6 = 384\pi \).

Answer:

\( \boldsymbol{\pi}((\boldsymbol{8})^{2}\boldsymbol{6})=\boldsymbol{384\pi} \) (or with multiplication sign as \( \pi((8)^{2}\times6)=384\pi \))