Marcus is making spherical soaps to sell in his online store. The surface area of a soap is 63.585in .^ 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? (1 point) 1.2in .*1.2 in.*1.2 in.; 2.25in .*2.25 in.*2.25 in.; 4.5in .*4.5 in.*4.5 in; 4in .*4 in.*4 in.
The formula for the surface area of a sphere is:
Surface Area = 4πr^2
Given that the surface area of the soap is 63.585in^2, we can set up the equation:
63.585 = 4πr^2
To find the radius (r), we can rearrange the equation:
r^2 = 63.585 / (4π) = 5.0778
r = sqrt(5.0778) = 2.25
So, the radius of the sphere is 2.25 inches.
Now, for the sphere to fit snugly inside the cube box, the diameter of the sphere must be equal to the length of the side of the cube box. Since the radius is 2.25 inches, the diameter is twice that:
Diameter = 2 * 2.25 = 4.5 inches
The dimensions of the cube box should be 4.5 inches * 4.5 inches * 4.5 inches.