I could really use some help with this problem because I'm pretty confused on what to do.
The formula for the volume of a cone is V=1/3(pi)r^2h where v represents volume, r represents the radius of the base, and h represents the height. What is the height of a cone with a volume of 66 cubic centimeters and a base with a radius of 3 centimeters?
V=1/3(3.14)r^2h
66=1/3(3.14)3^2h
66=9.42h
divide both side by 9.4
h=7.02
To find the height of a cone with a given volume and base radius, you can rearrange the formula for volume and solve for h. Here's how to do it:
1. Start with the formula for the volume of a cone: V = (1/3) * π * r^2 * h
2. Substitute the known values into the formula: V = 66 cm^3 and r = 3 cm. The formula now becomes: 66 = (1/3) * π * 3^2 * h.
3. Simplify the equation: 66 = (1/3) * π * 9 * h.
4. Divide both sides of the equation by π * 9 to isolate h: h = 66 / (π * 9).
5. Calculate the value of h: Using a calculator, divide 66 by π (pi), then divide the result by 9.
The value of h will be the height of the cone in centimeters, given a volume of 66 cubic centimeters and a base radius of 3 centimeters.