The volume of a cone is three hundred cubic kilometers. If the radius of the base is 9 kilometers, what is the height of the cone? Use three point one four for pi. Show your work and round to the nearest tenth.
V = 3.14r^2h /3 =
3.14*9^2*h / 3 = 300 km^3
Multiply both sides by 3,solve for L
3.14**81*L = 900
L = 900 / (3.14*81) = 3.5 km^3
let it bleed
To find the height of the cone, we can use the formula for the volume of a cone:
V = (1/3) * π * r^2 * h,
where V is the volume, π is 3.14 (approximately), r is the radius of the base, and h is the height of the cone.
Given that the volume V is 300 cubic kilometers and the radius r is 9 kilometers, we can rearrange the formula to solve for h:
300 = (1/3) * 3.14 * 9^2 * h.
Simplifying this equation, we have:
300 = (1/3) * 3.14 * 81 * h,
300 = 3.14 * 27 * h,
300 = 84.78 * h.
Now, we can divide both sides of the equation by 84.78 to isolate h:
h = 300 / 84.78.
Evaluating this, we find:
h ≈ 3.541 kilometers (rounded to the nearest tenth).
Therefore, the height of the cone is approximately 3.5 kilometers (rounded to the nearest tenth).