Final answer:
To find the radius of a cone with a height of 6 inches and a volume of 100.48 cubic inches, we use the formula for the volume of a cone which is rearranged to solve for the radius, yielding an approximate radius of 4 inches.
Step-by-step explanation:
The student is asking to find the radius of a cone with a given height and volume. The formula for the volume of a cone is V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height of the cone. We can solve for the radius (r) by rearranging the formula: r = √((3V)/(pi;h)).
Given that the cone is 6 inches tall and has a volume of 100.48 inches cubed, we can substitute these values into the equation:
- First, multiply the volume by 3: 100.48 * 3 = 301.44.
- Next, divide this product by the product of π and the height of the cone: 301.44 / (π * 6) = 301.44 / (3.14159 * 6) ≈ 16.0023.
- Then, take the square root of the result to find the radius: √(16.0023) ≈ 4 inches.
Therefore, the radius of the cone is approximately 4 inches.