Marcus is making spherical soaps to sell in his online store. The surface area of a soap is 63.585 in.2 and he wants to package them into a cube box so that it fits snugly. Using 3.14 as the value of pi, what should be the dimensions of the cube box?(1 point)
Responses
1.2 in. × 1.2 in. × 1.2 in.
1.2 inches times 1.2 inches times 1.2 inches
4 in.× 4 in.× 4 in.
4 inches times 4 inches times 4 inches
4.5 in. × 4.5 in. × 4.5 in.
4.5 inches times 4.5 inches times 4.5 inches
2.25 in. × 2.25 in. × 2.25 in.
2.25 inches times 2.25 inches times 2.25 inches
To find the dimensions of the cube box, we need to find the volume of the spherical soap and then calculate the side length of the cube box using the formula for the volume of a cube.
The formula for the surface area of a sphere is 4πr^2, where r is the radius of the sphere. Since the surface area of the soap is given as 63.585 in^2, we can set up the following equation:
4πr^2 = 63.585
Dividing both sides of the equation by 4π gives:
r^2 = 63.585 / (4π)
Using the value of π as 3.14, we can solve for the radius:
r^2 = 63.585 / (4*3.14)
r^2 = 5.08
r ≈ √(5.08)
r ≈ 2.25 inches
The dimensions of the cube box should be 2.25 inches × 2.25 inches × 2.25 inches.