What is the diameter of hemisphere with a volume of 9103 cm^3, to the nearest tenth of a centimeter?
The volume of a hemisphere can be calculated using the formula:
Volume = (2/3)πr^3
Where r is the radius of the hemisphere.
Given that the volume is 9103 cm^3, we can set up the equation:
9103 = (2/3)πr^3
Solving for r:
r^3 = (3/2)(9103/π)
r^3 ≈ (3/2) * (9103/3.14)
r^3 ≈ 4333.54
Taking the cube root of both sides:
r ≈ 15.68 cm
The diameter of the hemisphere is twice the radius, so the diameter is approximately:
2 * 15.68 ≈ 31.4 cm
Therefore, the diameter of the hemisphere is approximately 31.4 cm.
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The volume of a hemisphere can be calculated using the formula:
Volume = (2/3)πr^3
Given that the volume is 9103 cm^3, we can set up the equation:
9103 = (2/3)πr^3
Solving for r:
r^3 = (9103 * 3) / (2π)
r^3 ≈ 4326.287
Taking the cube root of both sides:
r ≈ 16.81 cm
The diameter of the hemisphere is twice the radius, so the diameter is approximately:
2 * 16.81 ≈ 33.62 cm
Therefore, the diameter of the hemisphere is approximately 33.62 cm to the nearest tenth of a centimeter.
To find the diameter of a hemisphere with a given volume, you need to use the volume formula for a hemisphere and solve for the diameter. The volume of a hemisphere is given by the formula V = (2/3)πr³, where V is the volume and r is the radius.
In this case, the given volume is 9103 cm³. We can set up the equation as follows:
9103 = (2/3)πr³
To solve for r, we need to isolate it. First, we can multiply both sides of the equation by (3/2) to remove the fraction:
(3/2) * 9103 = πr³
13654.5 = πr³
Next, divide both sides by π:
13654.5 / π = r³
Now, we can find the cube root of both sides to solve for r:
r = (13654.5 / π)^(1/3)
Using a calculator, you can evaluate this expression to find the radius r. Finally, to find the diameter, simply double the radius:
diameter = 2 * r
This will give you the diameter of the hemisphere to the nearest tenth of a centimeter.