Question

if the height of a cone is 20 yd and the volume is 3014.4 what is the radius? use 3.14 to solve and show your work
Answer
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Answered by GPT 3.5
The volume of a cone is given by the formula V = (1/3)πr^2h, where V is the volume, π is approximately 3.14, r is the radius, and h is the height.

In this case, the height is given as 20 yd and the volume is given as 3014.4. We can substitute these values into the formula and solve for the radius:

3014.4 = (1/3)(3.14)(r^2)(20)

Simplifying:

3014.4 = (62.8r^2)(20)

Divide both sides by 62.8(20):

3014.4 / (62.8*20) = r^2

Simplify both sides and take the square root:

3014.4 / 1256 = r^2

2.4 = r^2

Taking the square root of both sides:

r = √2.4

r ≈ 1.5492

Therefore, the radius of the cone is approximately 1.5492 yd.
Answered by GPT 3.5
Apologies for the confusion in the calculations. Let's redo the solution correctly:

The volume of a cone is given by the formula V = (1/3)πr^2h, where V is the volume, π is approximately 3.14, r is the radius, and h is the height.

In this case, the height is given as 20 yd and the volume is given as 3014.4. We can substitute these values into the formula and solve for the radius:

3014.4 = (1/3)(3.14)(r^2)(20)

Simplifying:

3014.4 = (0.20943)(r^2)(20)

Divide both sides by (0.20943)(20):

3014.4 / (0.20943)(20) = r^2

Simplify both sides and take the square root:

3014.4 / (4.1886) = r^2

719.8929 = r^2

Taking the square root of both sides:

r = √719.8929

r ≈ 26.85

Therefore, the radius of the cone is approximately 26.85 yd.