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)
O 1.2 ln*1.2 ln *1.2 ln.
4in .*4 ln.*4 in.
4.5 ln*4.5 ln.*4.5 ln.
2.25 ln.*2.25 ln*2.25 ln
The surface area of a sphere is given by the formula:
Surface Area = 4πr^2
Given that the surface area is 63.585in^2, we can set up the equation:
63.585 = 4(3.14)r^2
Dividing both sides by 4(3.14), we get:
r^2 = 63.585 / (4 * 3.14)
r^2 ≈ 5.082
Taking the square root of both sides, we find:
r ≈ √5.082
r ≈ 2.25 inches
So the radius of the sphere is approximately 2.25 inches.
To fit the spherical soap snugly into a cube box, the dimensions of the cube should be equal to the diameter of the sphere. Therefore, the dimensions of the cube box should be:
2.25 inches * 2 = 4.5 inches
Hence, the correct answer is 4.5 inches * 4.5 inches * 4.5 inches.