To find the dimensions of the cube box, we need to determine the length of each side, which will be the same for all sides of the cube.
The formula for the surface area of a sphere is:
Surface Area = 4πr^2
where r is the radius of the sphere.
Given that the surface area of the soap is 63.585 in.², we can set up the equation as follows:
63.585 = 4πr^2
Let's solve for r:
63.585 = 4 * 3.14 * r^2
Divide both sides by 4 * 3.14:
r^2 = 63.585 / (4 * 3.14)
r^2 = 5.0904
Take the square root of both sides to solve for r:
r = √5.0904
r ≈ 2.257 in
Now that we have the radius of the sphere, we can find the length of each side of the cube, which will be twice the radius:
Side length of cube = 2 * r
Side length of cube = 2 * 2.257
Side length of cube ≈ 4.514 in
Therefore, the dimensions of the cube box should be approximately 4.514 inches for 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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