To find the dimensions of the cube box, we first need to find the diameter of the spherical soap.
Surface area of a sphere = 4πr^2
63.585 in^2 = 4 * 3.14 * r^2
r^2 = 63.585 / (4 * 3.14)
r^2 = 5.06
r = √5.06
r = 2.25 in
Now, the diameter of the sphere is 2 * r = 2 * 2.25 = 4.5 in
For a sphere to fit snugly inside a cube, the diagonal of the cube should be equal to the diameter of the sphere.
Diagonal of a cube = √(3 * side length^2)
4.5 = √(3 * side length^2)
20.25 = 3 * side length^2
side length^2 = 20.25 / 3
side length^2 = 6.75
side length = √6.75
side length ≈ 2.60
Therefore, the dimensions of the cube box should be approximately 2.60 in x 2.60 in x 2.60 in. However, among the given options, the closest one is 2.25 in x 2.25 in x 2.25 in. So, the correct answer is:
2.25 in x 2.25 in x 2.25 in.
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.
4 in.× 4 in.× 4 in.
1.2 in. × 1.2 in. × 1.2 in.
4.5 in. × 4.5 in. × 4.5 in.
1 answer