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 4.5in .*4.5 in.*4.5 in.
O 1.2 ln.*1.2 ln.*1.2 ln.
O 4in .*4 in.*4 in.
O 2.25in * 2.25in .*2.25 in.
To find the dimensions of the cube box, we need to calculate the volume of the soap first. The surface area of a sphere is given by the formula 4πr^2, where r is the radius of the sphere.
In this case, the surface area of the soap is given as 63.585 in^2. So, we can set up the equation as:
4πr^2 = 63.585
Next, we can solve for the radius (r) by dividing both sides of the equation by 4π:
r^2 = 63.585 / (4π)
r^2 = 63.585 / (4 * 3.14)
r^2 ≈ 5.082
Taking the square root of both sides, we find:
r ≈ √5.082
r ≈ 2.256
Now, the dimensions of the cube box should be equal to the diameter of the spherical soap, which is twice the radius. So, the dimensions should be:
2 * r ≈ 2 * 2.256
≈ 4.512
Therefore, the closest answer is:
4.5 in. * 4.5 in. * 4.5 in.
So the correct option is:
O 4.5 in. * 4.5 in. * 4.5 in.
Why is it not 4.5 x 4.5 x 4.5?
To determine the dimensions of the cube box, we need to find the edge length of the cube.
The surface area of a sphere is given by the formula: A = 4πr^2.
We can rearrange the formula to solve for the radius, r: r = √(A / (4π)).
Substituting the given surface area, we have: r = √(63.585 / (4 * 3.14)) ≈ √5.067 ≈ 2.25 in.
The edge length of a cube is equal to twice the radius of the sphere. Therefore, the dimensions of the cube box should be: 2.25 in * 2.25 in * 2.25 in.
So the correct answer is: O 2.25in * 2.25in * 2.25in.