What is the volume of a sphere with a radius of 9.9 ft, rounded to the nearest tenth of a cubic foot?
The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius of the sphere.
Given that the radius of the sphere is 9.9 ft, we can plug this into the formula:
V = (4/3)π(9.9)^3
V ≈ 4856.8 cubic feet
Rounded to the nearest tenth of a cubic foot, the volume of the sphere is approximately 4856.8 cubic feet.
What is the diameter of a hemisphere with a volume of 2233, cm, cubed, comma2233 cm
3, to the nearest tenth of a centimeter?
The volume of a hemisphere is half the volume of a sphere with the same radius. The formula for the volume of a hemisphere is V = (2/3)πr^3, where r is the radius of the hemisphere.
Given that the volume of the hemisphere is 2233 cm^3, we can find the radius by rearranging the formula:
2233 = (2/3)πr^3
r^3 = (3/2) * 2233 / π
r ≈ (3/2) * 2233 / π)^(1/3)
Calculating this expression gives us the approximate radius of the hemisphere. To find the diameter, we double the radius.
d ≈ 2 * r
Plugging in the values and doing the calculations:
d ≈ 2 * ((3/2) * 2233 / π)^(1/3)
d ≈ 2 * ((3/2) * 2233 / π)^(1/3)
d ≈ 2 * ((3349.5 / π)^1/3)
d ≈ 2 * (308.47)
d ≈ 616.9
Therefore, the diameter of the hemisphere with a volume of 2233 cm^3 is approximately 616.9 cm, rounded to the nearest tenth of a centimeter.
Wrong
I apologize for the mistake. Let's correct it.
Given that the volume of a hemisphere is 2233 cm^3, we know that the volume of a sphere with radius "r" is V_sphere = (4/3)πr^3 and the volume of a hemisphere is half that, so V_hemisphere = (2/3)πr^3.
Given V_hemisphere = 2233 cm^3, we can set up the equation:
(2/3)πr^3 = 2233
r^3 = 2233 * (3/2) / π
r = ((2233 * 3 / 2) / π)^(1/3)
Now, we can find the diameter of the hemisphere:
Diameter = 2r
Diameter = 2 * ((2233 * 3 / 2) / π)^(1/3)
After calculating this, we get:
Diameter ≈ 21.6 cm
Therefore, the diameter of the hemisphere with a volume of 2233 cm^3 is approximately 21.6 cm, rounded to the nearest tenth of a centimeter.