Find the radius of a sphere with a volume of 1,767.1 m (3 cubed)
would I use the formula V=4/3*pie*radius (3 cubed)
yes
(4/3)π r^3 = 1767.1
r^3 = 21.864..
r = 7.4999 or appr 7.5 m
check:
(4/3)π(7.5)^3
=1767.145..
To find the radius of a sphere with a given volume, you can use the formula for the volume of a sphere:
V = (4/3) * π * r^3
Where:
V is the volume of the sphere,
π is a mathematical constant (approximately 3.14159), and
r is the radius of the sphere.
You are given a volume of 1,767.1 m^3. Let's solve for the radius:
1,767.1 = (4/3) * π * r^3
To isolate the radius, we can rearrange the equation:
r^3 = (3/4) * (1,767.1 / π)
Now, let's simplify the right side of the equation:
r^3 = 1,767.1 / (4/3π)
r^3 = 1,767.1 / (12/12π)
r^3 = 1,767.1 / (12π/12)
r^3 = (1,767.1 * 12) / (12π)
r^3 = (21,205.2) / (12π)
Now, we can calculate the cube root of both sides to solve for r:
r = (21,205.2 / (12π))^(1/3)
Using a calculator, you can evaluate this expression to find the radius of the sphere.
Yes, you're on the right track! The formula for the volume of a sphere is V = (4/3)πr^3, where V is the volume and r is the radius.
To find the radius of a sphere with a volume of 1,767.1 m^3, we can rearrange the formula and solve for radius.
1. Start with the formula: V = (4/3)πr^3
2. Substitute the given volume: 1,767.1 = (4/3)πr^3
3. Divide both sides by (4/3)π to isolate the radius:
1,767.1 / ((4/3)π) = r^3
4. Simplify the equation on the left side:
1,767.1 / ((4/3)π) = r^3
(1,767.1 * 3) / (4π) = r^3
5301.3 / (4π) = r^3
5. Now, find the cube root of both sides to solve for the radius:
∛(5301.3 / (4π)) = r
By evaluating the cube root of (5301.3 / (4π)), you will find the radius of the sphere.