Question

The volume of a sphere, V, is calculated using the formula V = (4/3)πr³, where r is the radius of the sphere. Rearrange the formula to solve for the radius (r). What is the radius of a sphere with a volume of 100 ft³? (Round your answer to the nearest hundredth.)

Answer 1

r ≈ 2.88 ft

Step-by-step explanation:

given the formula for the volume of a sphere

V =
`(4)/(3)` πr³ ( r is the radius ) ← multiply both sides by 3

3V = 4πr³ ( divide both sides by 4π )

`(3V)/(4\pi )` = r³ ( take cube root of both sides )

`\sqrt[3]{(3V)/(4\pi ) }` =
`\sqrt[3]{r^3}`

`\sqrt[3]{(3V)/(4\pi ) }` = r

given V = 100 ft³ , then

r =
`\sqrt[3]{(3V)/(4\pi ) }` =
`\sqrt[3]{(3(100))/(4\pi ) }` =
`\sqrt[3]{(300)/(4\pi ) }` ≈ 2.88 ft ( to the nearest hundredth )

Answer 2

To solve for the radius (r) in the volume formula of a sphere, rearrange the formula and solve for r by dividing both sides by (4/3)π, then take the cube root.

Step-by-step explanation:

To solve for the radius (r) in the formula V = (4/3)πr³, you need to rearrange the formula. Start by dividing both sides of the equation by (4/3)π: V / ((4/3)π) = r³. Simplify the left side of the equation: (3V) / (4π) = r³. Take the cube root of both sides to solve for r: r = (3V / (4π))^(1/3).

For the given volume of 100 ft³, plug it into the formula and solve for r: r = (3(100) / (4π))^(1/3) = (300 / (4π))^(1/3) = (75 / π)^(1/3) ≈ 2.67 ft.