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
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.
To find the dimensions of the cube box, we need to find the edge length of the cube.
The surface area of a sphere is given by the formula:
A = 4πr²
Given that the surface area of the soap is 63.585 in²,
63.585 = 4(3.14)(r²)
Dividing both sides by 4(3.14) gives:
r² = 5.091
Taking the square root of both sides gives:
r = 2.259
Since the soap is spherical and we need the dimensions for a cube, the edge length of the cube should equal the diameter of the sphere, which is 2r:
2(2.259) = 4.518
So, the dimensions of the cube box should be approximately 4.5 in. × 4.5 in. × 4.5 in.