Problem 24
Question
Find the volume of a cone with a radius of 6 in. and a height of 13 in
Step-by-Step Solution
Verified Answer
The volume of the cone is approximately 490.088 cubic inches.
1Step 1 - Identify the formula for the volume of a cone
The volume of a cone is calculated using the formula: \[ V = \frac{1}{3} \pi r^2 h \] where \( V \) is the volume, \( r \) is the radius of the base, and \( h \) is the height of the cone.
2Step 2 - Substitute the given values into the formula
Substitute the given radius \( r = 6 \) inches and height \( h = 13 \) inches into the formula: \[ V = \frac{1}{3} \pi (6)^2 (13) \]
3Step 3 - Simplify the expression
Calculate the area of the base: \[ (6)^2 = 36 \] Multiply by the height: \[ 36 \times 13 = 468 \] Then multiply by \( \frac{1}{3} \): \[ \frac{1}{3} \times 468 = 156 \] Hence, the volume is: \[ V = 156 \pi \]
4Step 4 - Provide the numerical answer
Using the value of \( \pi \approx 3.1416 \), calculate the volume: \[ V \approx 156 \times 3.1416 \approx 490.088 \] Therefore, the volume of the cone is approximately 490.088 cubic inches.
Key Concepts
cone volume formula
cone volume formula
Understanding how to find the volume of a cone starts with knowing the formula. The formula to calculate the volume is:
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