The volume of a sphere is 523 ππ3. What is the approximate measure of the radius?
4/3 Οr^3 = 523
r^3 = 523* 3/(4Ο) = 1569/(4Ο) = 124.85 β 125
r β 5
To find the radius of a sphere with a given volume, we can use the formula for the volume of a sphere:
π = (4/3)ππ^3,
where π is the volume and π is the radius.
Given that the volume of the sphere is 523 ππ^3, we can write the equation as:
523 = (4/3)ππ^3.
To find the radius, we can rearrange the equation:
π^3 = (3/4)Γ(523/π).
Taking the cube root of both sides, we get:
π = β[(3/4)Γ(523/π)].
Now we can approximate the value by plugging it into a calculator:
π β β[(3/4)Γ(523/π)] β 4.32 ππ (rounded to two decimal places).
Therefore, the approximate measure of the radius is 4.32 cm.
To find the approximate measure of the radius of a sphere given its volume, you can use the formula for the volume of a sphere:
V = (4/3)Οr^3
Here, V represents the volume and r represents the radius of the sphere.
For this problem, we are given that the volume of the sphere is 523 cm^3. So, we can set up the equation and solve for r:
523 = (4/3)Οr^3
To find the approximate measure of the radius, we need to isolate r.
First, divide both sides of the equation by (4/3)Ο:
523 / ((4/3)Ο) = r^3
Now, to find the cube root of both sides to solve for r:
r = (523 / ((4/3)Ο))^(1/3)
Plug in the value of Ο (pi), which is approximately 3.14159, and calculate the expression on the right side:
r β (523 / ((4/3) * 3.14159))^(1/3)
Simplify further:
r β (523 / (4.18879))^(1/3)
r β 5.98691
Therefore, the approximate measure of the radius is approximately 5.99 cm.