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
4.5 in. × 4.5 in. × 4.5 in.
4.5 inches times 4.5 inches times 4.5 inches
1.2 in. × 1.2 in. × 1.2 in.
1.2 inches times 1.2 inches times 1.2 inches
4 in.× 4 in.× 4 in.
4 inches times 4 inches times 4 inches
2.25 in. × 2.25 in. × 2.25 in.
2.25 inches times 2.25 inches times 2.25 inches
To find the dimensions of the cube box, we need to first find the radius of the spherical soap.
The formula for the surface area of a sphere is given by 4πr², where r is the radius of the sphere.
We can rearrange this formula to solve for the radius:
4πr² = 63.585
r² = 63.585 / (4π)
r² = 5.0625 / π
r ≈ √(5.0625 / 3.14)
r ≈ 1.27538
Now, we can use this radius to find the dimensions of the cube box. Since the sphere will fit snugly inside the cube, the side length of the cube will be equal to the diameter of the sphere.
d = 2r
d = 2 * 1.27538
d ≈ 2.55076
Therefore, the dimensions of the cube box should be approximately 2.55076 inches × 2.55076 inches × 2.55076 inches.
Rounded to the nearest decimal place, this gives us the option:
2.25 in. × 2.25 in. × 2.25 in.