The volume of a sphere is 3,000ð m3. What is the surface area of the sphere to the nearest square meter?
To find the surface area of a sphere, we can use the formula:
Surface Area = 4πr^2
where r is the radius of the sphere.
Given that the volume of the sphere is 3,000π m^3, we can find the radius using the volume formula:
Volume = (4/3)πr^3
Rearranging the formula to solve for r:
r = ∛((3/4)Volume/π)
Substituting the given volume:
r = ∛((3/4)(3,000π)/π)
Simplifying:
r = ∛(9,000/4)
r = ∛2,250
r ≈ 13.42 m (rounded to two decimal places)
Now that we have the radius, we can find the surface area:
Surface Area = 4π(13.42)^2
Surface Area ≈ 2,264.88 m^2 (rounded to the nearest square meter)
Therefore, the surface area of the sphere to the nearest square meter is approximately 2,264 m^2.
To find the surface area of a sphere, we need to know its radius. However, the question only provides the volume of the sphere.
To find the radius of the sphere, we can use the formula for the volume of a sphere:
V = (4/3)πr3,
where V is the volume and r is the radius of the sphere. In this case, the volume is given as 3,000π m³.
Let's rearrange the formula to solve for r:
r³ = (3V) / (4π),
Now we can substitute the given value of V:
r³ = (3 * 3000π) / (4π),
r³ = 9,000 / 4,
r³ = 2,250.
Now we can find the cube root of both sides to get the value of r:
r ≈ ∛2,250 ≈ 12.63.
So, the radius of the sphere is approximately 12.63 meters.
Now, we can find the surface area. The formula for the surface area of a sphere is given by:
A = 4πr²,
where A is the surface area and r is the radius.
Substituting the value of r:
A = 4π(12.63)² ≈ 4π(159.42) ≈ 633.22π.
To find the surface area to the nearest square meter, we need to calculate the value of π and round the result to the nearest whole number.
Using the value of π as 3.14:
A ≈ 633.22 * 3.14 ≈ 1,988.40.
Therefore, the surface area of the sphere is approximately 1,988 square meters.
(4/3)pi r^3 = 3,000
r^3 = 9000/(4 pi)
r = [9000/(4 pi)]^(1/3)
4 pi r^2 = 4 pi [9000/(4 pi)]^(2/3)