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
2.25 in. × 2.25 in. × 2.25 in.
2.25 inches times 2.25 inches times 2.25 inches
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.
To find the dimensions of the cube box, we need to consider the surface area of the soap, which is a sphere.
The formula for the surface area of a sphere is: A = 4πr², where A is the surface area and r is the radius of the sphere.
Given that the surface area of the soap is 63.585 in², we can set up the equation: 63.585 = 4πr²
To solve for r, we divide both sides of the equation by 4π: r² = 63.585 / (4π)
Now, we can find the value of r by taking the square root of both sides of the equation: r = √(63.585 / (4π)) ≈ √(5.06) ≈ 2.25
Therefore, the radius of the soap is approximately 2.25 inches.
Since we want to package the soap into a cube box, all sides of the cube should have the same length, which is equal to the diameter of the soap (2r).
So, the dimensions of the cube box should be 2.25 in. × 2.25 in. × 2.25 in.
Therefore, the correct answer is:
2.25 in. × 2.25 in. × 2.25 in.