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
4.5 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
4 in.× 4 in.× 4 in.
To find the dimensions of the cube box, we need to consider the volume of the spherical soap. The formula for the surface area of a sphere is:
Surface Area = 4πr^2
Given that the surface area of the soap is 63.585 in.2, we can solve for the radius (r):
63.585 = 4πr^2
r = √(63.585 / (4π))
r ≈ √(63.585 / (4 * 3.14))
r ≈ √(63.585 / 12.56)
r ≈ √5.07
r ≈ 2.25
Now, we have the radius of the sphere as 2.25 inches. The diameter (d) is twice the radius:
d = 2 * 2.25
d = 4.5 inches
Since a cube box can snugly fit a sphere with the same side length as its own, the dimensions of the cube box should be 4.5 inches × 4.5 inches × 4.5 inches.
Therefore, the correct answer is:
4.5 in. x 4.5 in. x 4.5 in.