Question

The volume, ( V ), of a cone is calculated using the formula ( V = /{1}/{3} pi r² h ), where ( r ) is the radius of the base and ( h ) is the height of the cone. Rearrange the formula to solve for the radius ((r )).

a) ( r = sqrt{/{3V}/{pi h}}
b) ( r = sqrt{/{V}/{3pi h}}
c) ( r = sqrt{/{V}/{pi 3h}}
d) ( r = sqrt{/{3V}/{hpi}}

Answer 1

To find the radius (r) from the cone's volume formula, multiply the formula by 3, then divide by πh, and finally take the square root of the result, yielding the correct formula: r = √(3V / (πh)).

Step-by-step explanation:

To solve for the radius (r) in the volume formula of a cone V = 1/3 π r² h, we need to isolate r. Here are the steps we'll take:

1. Multiply both sides of the equation by 3 to get rid of the fraction: 3V = π r² h.
2. Divide both sides by πh to move them to the other side of the equation: 3V / (πh) = r².
3. Finally, take the square root of each side to solve for r: r = √(3V / (πh)).

Looking at the options provided, the correct rearranged formula would be (a): r = √(3V / (πh)), exemplifying the process of isolating the radius in the cone's volume formula to facilitate radius calculations.