Question

problem #3
calculate the volume of each cylinder.
here is the link to the staar reference sheet (formula sheet)
enter your answers in the table.
then press \check my work.\
volume
prism or cylinder
v = bh
pyramid or cone
v = \\(\frac{1}{3}\\)bh
sphere
v = \\(\frac{4}{3}\\)\\(\pi r^3\\)

	volume (cubic units)
right cylinder

check my work

Explanation:

Step1: Identify the formula for the volume of a cylinder

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

Step2: Calculate the volume of the Left Cylinder

For the Left Cylinder, the radius \( r = 3 \) and the height \( h = 8 \).
Substitute these values into the formula:
\( V = \pi \times 3^2 \times 8 \)
\( V = \pi \times 9 \times 8 \)
\( V = 72\pi \)
Using \( \pi \approx 3.14 \), we get \( V \approx 72 \times 3.14 = 226.08 \approx 226.2 \) (matches the given value).

Step3: Calculate the volume of the Right Cylinder

For the Right Cylinder, the diameter is \( 4 \), so the radius \( r = \frac{4}{2} = 2 \), and the height \( h = 6 \).
Substitute these values into the formula:
\( V = \pi \times 2^2 \times 6 \)
\( V = \pi \times 4 \times 6 \)
\( V = 24\pi \)
Using \( \pi \approx 3.14 \), we get \( V \approx 24 \times 3.14 = 75.36 \)

Answer:

• Left Cylinder Volume: \( 72\pi \) (or approximately \( 226.2 \) cubic units)
• Right Cylinder Volume: \( 24\pi \) (or approximately \( 75.36 \) cubic units)