Questions: The volume of a cone with height h and radius r can be found using the formula V=1/3 π r^2 h Find the volume of a cone with radius 7 feet and height 4 feet. ft^3

Solution Steps

To find the volume of a cone, we can use the formula \( V = \frac{1}{3} \pi r^2 h \). Given the radius \( r = 7 \) feet and height \( h = 4 \) feet, we can substitute these values into the formula to calculate the volume.

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

Given:

• Radius \( r = 7 \) feet
• Height \( h = 4 \) feet

Substitute these values into the formula: \[ V = \frac{1}{3} \pi (7)^2 (4) \]

First, calculate \( 7^2 \): \[ 7^2 = 49 \]

Next, multiply by the height \( 4 \): \[ 49 \times 4 = 196 \]

Then, multiply by \( \frac{1}{3} \): \[ \frac{1}{3} \times 196 = 65.3333 \]

Finally, multiply by \( \pi \): \[ V = 65.3333 \times \pi \approx 205.2507 \]

Final Answer