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)
○ 2.25 in. x 2.25 in. x 2.25 in.
4 in. 4 in. x 4 in.
4.5 in. x 4.5 in. x 4.5 in.
1.2 in. x 1.2 in. x 1.2 in.
To find the dimensions of the cube box, we need to find the length of one side of the cube.
The surface area of a sphere is given by the formula: 4πr², where r is the radius of the sphere.
Given that the surface area of the soap is 63.585 in², we can set up the equation:
4πr² = 63.585
We are given the value of pi as 3.14, so we can substitute that in:
4(3.14)r² = 63.585
Divide both sides by 4(3.14):
r² = 63.585 / (4(3.14))
r² = 5.0848
Take the square root of both sides to find the radius:
r = √(5.0848)
r ≈ 2.25
Since the side length of the cube should be twice the radius, the dimensions of the cube box should be:
2.25 in. x 2.25 in. x 2.25 in.