Marcus is making spherical soaps to sell in his online store. The surface area of a soap is 63.585 in." 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)
• 4 in. x 4 in. x 4 in.
• 4.5 in. × 4.5 in. × 4.5 in.
• 1.2 in. × 1.2 in. x 1.2 in.
• 2.25 in. x 2.25 in. × 2.25 in.
The formula for the surface area of a sphere is given by A = 4πr^2, where r is the radius of the sphere. In this case, the surface area of the soap is 63.585 in^2. Therefore, we can set up the equation:
4πr^2 = 63.585
Dividing both sides by 4π gives:
r^2 = 63.585 / (4π)
r^2 = 4.032
Taking the square root of both sides gives:
r = √(4.032)
r ≈ 2.01
The diameter of the sphere is equal to 2 times the radius, so the diameter is approximately 4.02 inches.
Now, let's consider the cube box. To fit snugly, the soap's diameter should be equal to the length of one side of the cube. Therefore, the dimensions of the cube box should be approximately 4.02 inches x 4.02 inches x 4.02 inches.
Thus, the closest option is "4 in. x 4 in. x 4 in."