To find the dimensions of the cube box, we need to first determine the radius of the soap.
The surface area of a sphere is given by the formula: surface area = 4πr^2, where r is the radius of the sphere.
Substituting the given surface area (63.585 in.²) into the formula:
63.585 in.² = 4πr^2
Dividing both sides of the equation by 4π will give us the value of r^2:
r^2 = 63.585 in.² / (4π)
Using pi as approximately 3.14, we can calculate r^2:
r^2 = 63.585 in.² / (4 * 3.14)
r^2 = 5.0725 in.²
To find the radius, we take the square root of both sides:
r = sqrt(5.0725 in.²)
r ≈ 2.25 in.
Since a cube has all sides equal, the dimensions of the cube box should be 2 times the radius of the soap, which is approximately:
2 * 2.25 in. ≈ 4.5 in.
Therefore, the dimensions of the cube box should be approximately 4.5 inches on each side.
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?
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