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
4.5 in. × 4.5 in. × 4.5 in.
4.5 inches times 4.5 inches times 4.5 inches
4 in.× 4 in.× 4 in.
4 inches times 4 inches times 4 inches
2.25 in. × 2.25 in. × 2.25 in.
2.25 inches times 2.25 inches times 2.25 inches
1.2 in. × 1.2 in. × 1.2 in.
To find the dimensions of the cube box, we need to calculate the side length of the cube.
The formula for the surface area of a sphere is given by 4πr^2, where r is the radius of the sphere.
Given that the surface area of the soap is 63.585 in^2, we can set up the equation:
4πr^2 = 63.585
Dividing both sides by 4 and π:
r^2 = 63.585 / (4π)
r^2 = 63.585 / (4 * 3.14)
r^2 ≈ 5.091
Taking the square root of both sides:
r ≈ √5.091
r ≈ 2.258
Since the cube box should fit the sphere snugly, each side of the cube should be equal to the diameter of the sphere.
The diameter of the sphere is 2 * r:
d ≈ 2 * 2.258
d ≈ 4.516
Therefore, the dimensions of the cube box should be approximately 4.5 inches × 4.5 inches × 4.5 inches.
So, the correct response is: 4.5 in. × 4.5 in. × 4.5 in.