Question

what is the volume of this cone? round your answer to the nearest hundredth. 19 yd 14 yd cubic yards submit

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 of the base and \( h \) is the height of the cone.

Step2: Determine the radius and height

From the diagram, the diameter of the base is \( 14 \) yd, so the radius \( r = \frac{14}{2} = 7 \) yd. The height \( h = 19 \) yd.

Step3: Substitute the values into the formula

Substitute \( r = 7 \) and \( h = 19 \) into the formula:

$$ V = \frac{1}{3} \pi (7)^2 (19) $$

First, calculate \( 7^2 = 49 \). Then:

$$ V = \frac{1}{3} \pi (49)(19) $$

Calculate \( 49 \times 19 = 931 \). So:

$$ V = \frac{1}{3} \pi (931) $$

$$ V = \frac{931}{3} \pi $$

Using \( \pi \approx 3.14159 \):

$$ V \approx \frac{931}{3} \times 3.14159 $$

Calculate \( \frac{931}{3} \approx 310.3333 \). Then:

$$ V \approx 310.3333 \times 3.14159 \approx 974.02 $$

Answer:

\( 974.02 \)