Question

cylinder a has twice the height of cylinder b. cylinder b has twice the radius of cylinder a.

(image of cylinder a: r=2, h=10; image of cylinder b: r=4, h=5)

use the drop-down menus to compare the volume of the cylinders.

cylinder a’s volume is drop-down cubic units. cylinder b’s volume is drop-down cubic units.
cylinder a’s volume is drop-down as cylinder b’s volume.

Explanation:

Step1: Recall Cylinder Volume Formula

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

Step2: Calculate Volume of Cylinder A

For Cylinder A, \( r = 2 \) and \( h = 10 \). Substitute into the formula:
\( V_A = \pi \times (2)^2 \times 10 = \pi \times 4 \times 10 = 40\pi \approx 125.66 \) (cubic units, using \( \pi \approx 3.14 \): \( 40 \times 3.14 = 125.6 \)).

Step3: Calculate Volume of Cylinder B

For Cylinder B, \( r = 4 \) and \( h = 5 \). Substitute into the formula:
\( V_B = \pi \times (4)^2 \times 5 = \pi \times 16 \times 5 = 80\pi \approx 251.33 \) (cubic units, using \( \pi \approx 3.14 \): \( 80 \times 3.14 = 251.2 \)).

Step4: Compare Volumes

To find the relationship between \( V_A \) and \( V_B \), divide \( V_A \) by \( V_B \):
\( \frac{V_A}{V_B} = \frac{40\pi}{80\pi} = \frac{1}{2} \). So \( V_A \) is half of \( V_B \).

Answer:

Cylinder A's volume is \( 40\pi \) (or ~125.6) cubic units. Cylinder B's volume is \( 80\pi \) (or ~251.2) cubic units. Cylinder A’s volume is half as Cylinder B’s volume.

(If numerical approximations are preferred:
Cylinder A: \( 125.6 \) (or \( 40\pi \)), Cylinder B: \( 251.2 \) (or \( 80\pi \)), and the relationship is "half".)