Question

The volume of a sphere can be given by the formula V = 4/3Ï€r^3. You have to design a spherical container that will hold a volume of 55 cubic inches. What should the radius (r) of your container be?

Answer 1

To find the radius of the container, we rearrange the formula for the volume of a sphere and solve for r. The volume formula is V = 4/3πr^3. By isolating r, we can determine that r is approximately 2.212 inches.

Step-by-step explanation:

To find the radius of the container, we can rearrange the formula for the volume of a sphere. The formula is V = (4/3)πr^3, where V is the volume and r is the radius. In this case, we want to find r when V is 55 cubic inches. We can rewrite the formula as: (4/3)πr^3 = 55. To solve for r, we need to isolate it.

First, we can multiply both sides of the equation by (3/4) to get rid of the fraction: πr^3 = (55)(3/4). Then, divide both sides by π: r^3 = (55)(3/4) / π. Finally, take the cube root of both sides to get the value of r: r = √( (55)(3/4) / π ).

Using a calculator, we can evaluate the expression and find that r is approximately 2.212 inches.