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 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
1.2 in. × 1.2 in. × 1.2 in.
1.2 inches times 1.2 inches times 1.2 inches
2.25 in. × 2.25 in. × 2.25 in.
The surface area of a sphere is given by the formula:
SA = 4πr^2
where SA is the surface area and r is the radius of the sphere.
Let's solve for r:
63.585 = 4(3.14)r^2
63.585 = 12.56r^2
r^2 = 5.08
r ≈ √5.08
r ≈ 2.25
Since the cube box should fit snugly around the soap, the dimensions of the box should be equal to the diameter of the soap, which is 2 times the radius.
So, the dimensions of the cube box should be 2.25 inches × 2.25 inches × 2.25 inches.
Therefore, the correct response is:
2.25 in. × 2.25 in. × 2.25 in.