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.
To find the dimensions of the cube box, we need to calculate the volume of the soap and then find the side length of the cube box.
The surface area of a sphere is given by the formula: 4πr^2, where r is the radius of the sphere.
Using this formula, we can find the radius of the soap as follows:
63.585 in. = 4πr^2
Dividing both sides by 4π, we get:
r^2 = 63.585 in. / (4π)
r^2 = 5.091 in.
Taking the square root of both sides, we get:
r ≈ 2.256 in.
The diameter of the sphere is twice the radius, so the diameter is approximately:
d = 2 * 2.256 in. ≈ 4.512 in.
Now, we can calculate the volume of the sphere using the formula: (4/3)πr^3:
volume ≈ (4/3)π * (2.256 in.)^3
volume ≈ 4.208 in.^3
Since the cube box needs to fit the sphere snugly, the side length of the cube box should be equal to the diameter of the sphere, which is approximately 4.512 in.
Therefore, the correct answer is:
• 4.5 in. × 4.5 in. × 4.5 in.