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?(1 point)
Responses
1.2 in. × 1.2 in. × 1.2 in.
1.2 inches times 1.2 inches times 1.2 inches
2.25 in. × 2.25 in. × 2.25 in.
2.25 inches times 2.25 inches times 2.25 inches
4 in.× 4 in.× 4 in.
4 inches times 4 inches times 4 inches
4.5 in. × 4.5 in. × 4.5 in.
To find the dimensions of the cube box that can snugly fit a spherical soap, we need to find the edge length of the cube.
The surface area of a sphere is given by the formula: 4πr^2, where r is the radius of the sphere.
In this case, we know that the surface area of the soap is 63.585 in^2, so we can set up the equation as follows:
4πr^2 = 63.585
To solve for r, we divide both sides of the equation by 4π:
r^2 = 63.585 / (4π)
r^2 ≈ 5.087
Taking the square root of both sides, we find:
r ≈ 2.259
Since the edge length of the cube is twice the radius of the sphere, the dimensions of the cube box should be approximately:
2.259 in. × 2.259 in. × 2.259 in.
So, the correct answer is option 2: 2.25 in. × 2.25 in. × 2.25 in.