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
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.
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.
To find the dimensions of the cube box, we need to find the side length of the cube. Since the soap is spherical, we can use the formula for the surface area of a sphere to find the radius of the soap.
Surface area of a sphere = 4πr^2
Given the surface area of the soap is 63.585 in^2, we can plug it into the formula:
63.585 = 4πr^2
Dividing both sides by 4π, we get:
r^2 = 63.585 / (4 × 3.14)
r^2 ≈ 5.092
Taking the square root of both sides, we get:
r ≈ √5.092
r ≈ 2.257
So the radius of the soap is approximately 2.257 inches.
Since all sides of the cube will have the same length, the dimensions of the cube should be approximately:
2 × radius = 2 × 2.257 ≈ 4.514 inches
Therefore, the closest option is 4.5 in. × 4.5 in. × 4.5 in.