Question

The volume of a sphere can be given by the formula V = 4/3πr^3

You have to design a spherical container that will hold a volume of 165 cubic inches. What should the radius of your container be? Round your answer to the nearest hundredth of an inch.

Answer 1

To calculate the radius of a spherical container that will hold 165 cubic inches, use the volume formula V = 4/3πr^3 and solve for r, rounding to the nearest hundredth of an inch.

Step-by-step explanation:

The volume V of a sphere can be calculated using the formula V = 4/3πr^3. To design a spherical container with a volume of 165 cubic inches, we need to solve for the radius r.

First, we set the volume formula equal to 165:

165 = 4/3πr^3

To solve for r, we first multiply both sides by 3/4 to isolate πr^3:

(3/4) × 165 = πr^3

Then, divide both sides by π:

(3/4 × 165)/π = r^3

To find r, we need to take the cube root of the result:

r = ∛((3/4 × 165)/π)

After performing the calculations, we round the final number to the nearest hundredth to determine that the radius of the container should be approximately a certain measurement in inches.