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 first need to find the radius of the soap.
The surface area of a sphere is given by the formula: 4πr^2, where r is the radius of the sphere.
So, 4πr^2 = 63.585 in.
Dividing both sides of the equation by 4π, we get:
r^2 = 63.585 in / 4π
r^2 = 5.0625 in
Taking the square root of both sides, we get:
r = √5.0625 in
r ≈ 2.25 in
The diameter of the soap is twice the radius, so the diameter is approximately 2 * 2.25 in = 4.5 in.
To fit the soap snugly into the cube box, each side of the cube should have a length equal to the diameter of the soap.
Therefore, the correct dimensions of the cube box should be:
4.5 in. × 4.5 in. × 4.5 in.