What is the diameter of a hemisphere with a volume of 8514, cm^3

, to the nearest tenth of a centimeter

3 answers

To find the diameter of a hemisphere with a volume of 8514 cm^3, we first need to find the radius of the hemisphere.

The formula for the volume of a hemisphere is:

V = (2/3) * π * r^3

Given that the volume V is 8514 cm^3, we can plug in this value and solve for the radius r:

8514 = (2/3) * π * r^3
r^3 = (3/2) * (8514 / π)
r = (3/2)^(1/3) * (8514 / π)^(1/3)
r ≈ 18.4 cm

Now that we have the radius, we can find the diameter by multiplying the radius by 2:

D = 2 * r
D = 2 * 18.4
D = 36.8 cm

Therefore, the diameter of the hemisphere with a volume of 8514 cm^3 is approximately 36.8 cm.
wrong
I apologize for the mistake in my calculation. Let me correct it:

Given that the volume of the hemisphere is 8514 cm^3, the formula for the volume of a hemisphere is:

V = (2/3) * π * r^3

We can rearrange the formula to solve for the radius:

r = ((3 * V) / (4 * π))^(1/3)
r = ((3 * 8514) / (4 * π))^(1/3)
r ≈ 14.3 cm

The diameter of the hemisphere is twice the radius:

D = 2 * 14.3
D ≈ 28.6 cm

Therefore, the diameter of the hemisphere with a volume of 8514 cm^3 is approximately 28.6 cm.