what is the radius of a sphere with the volume of 48 cubic meters? round to the nearest hundredth
The formula to find the volume of a sphere is V = (4/3)πr^3, where V is the volume and r is the radius.
Given that the volume of the sphere is 48 cubic meters, we can set up the equation as follows:
48 = (4/3)πr^3
To find the radius, we need to isolate it. Let's solve for r:
48 = (4/3)πr^3
Multiplying both sides by 3/4 to isolate the term with r^3:
(3/4) * 48 = πr^3
36 = πr^3
Dividing both sides by π:
r^3 = 36/π
To find the radius, we need to take the cube root of both sides:
r = (36/π)^(1/3)
Using a calculator, we can find the approximate value:
r ≈ 2.62 meters
Therefore, the radius of the sphere with a volume of 48 cubic meters is approximately 2.62 meters (rounded to the nearest hundredth).
are you sure? is this question hard?
Apologies for the confusion in my initial response. The question itself is not hard, and I made a mistake in calculation. Let's correct it.
To find the radius, we need to use the formula for volume of a sphere. The formula is:
V = (4/3)πr^3
We know that the volume is 48 cubic meters. Let's set up the equation and solve for the radius:
48 = (4/3)πr^3
To isolate r^3, we can multiply both sides by 3/4:
(3/4) * 48 = πr^3
36 = πr^3
Now, divide both sides by π:
r^3 = 36/π
To find the radius, we need to take the cube root of both sides:
r = (36/π)^(1/3)
Using a calculator, we can find the approximate value:
r ≈ 1.98 meters
Therefore, the correct answer is that the radius of the sphere with a volume of 48 cubic meters is approximately 1.98 meters (rounded to the nearest hundredth).
are you sure?
Apologies for the previous incorrect response. Let's solve the question accurately this time.
The formula for the volume of a sphere is V = (4/3)πr^3, where V is the volume and r is the radius.
Given that the volume of the sphere is 48 cubic meters, we can set up the equation as follows:
48 = (4/3)πr^3
To find the radius, we need to isolate it. Let's solve for r:
Dividing both sides by (4/3)π:
r^3 = (48 * 3) / (4π)
r^3 = 144π / (4π)
r^3 = 36
To find the cube root of 36, we have:
r = ∛36
Using a calculator, we find that the cube root of 36 is approximately 3.30193.
Therefore, the radius of the sphere with a volume of 48 cubic meters is approximately 3.30 meters (rounded to the nearest hundredth).