Question

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

use the drop - down menus to compare the volume of the cylinders.
cone a’s volume is ▼ cubic units. cone b’s volume is ▼ cubic units.
cone a’s volume is ▼ as cone b’s volume.

Explanation:

Step1: Recall the volume formula for a cone

The volume \( V \) of a cone is given by the formula \( V = \frac{1}{3}\pi r^2 h \), where \( r \) is the radius and \( h \) is the height.

Step2: Calculate the volume of Cone A

For Cone A, \( r = 2 \) and \( h = 12 \). Substitute these values into the formula:

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If we take \( \pi \approx 3.14 \), then \( V_A \approx 16 \times 3.14 = 50.24 \) cubic units.

Step3: Calculate the volume of Cone B

For Cone B, \( r = 4 \) and \( h = 6 \). Substitute these values into the formula:

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$$

If we take \( \pi \approx 3.14 \), then \( V_B \approx 32 \times 3.14 = 100.48 \) cubic units.

Step4: Compare the volumes of Cone A and Cone B

To find the relationship between \( V_A \) and \( V_B \), we can divide \( V_A \) by \( V_B \):

$$ \frac{V_A}{V_B} = \frac{16\pi}{32\pi} = \frac{1}{2} $$

So, Cone A's volume is half of Cone B's volume.

Answer:

Cone A's volume is \( 16\pi \) (or approximately \( 50.24 \)) cubic units. Cone B's volume is \( 32\pi \) (or approximately \( 100.48 \)) cubic units. Cone A's volume is half as Cone B's volume.