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
4 in.× 4 in.× 4 in.
4 inches times 4 inches times 4 inches
1.2 in. × 1.2 in. × 1.2 in.
1.2 inches times 1.2 inches times 1.2 inches
4.5 in. × 4.5 in. × 4.5 in.
To find the dimensions of the cube box, we need to calculate the edge 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.
Surface area of sphere = 4πr²
63.585 in.² = 4 * 3.14 * r²
r² = 63.585 in.² / (4 * 3.14)
r² = 5.072 in.²
r ≈ √5.072
r ≈ 2.25 in.
Since a sphere can be perfectly inscribed within a cube, the diameter of the sphere (2 * r) will be equal to the edge length of the cube. Therefore, the dimensions of the cube box should be 2.25 in. × 2.25 in. × 2.25 in.
Therefore, the correct answer is:
2.25 in. × 2.25 in. × 2.25 in.