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 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
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.
To find the dimensions of the cube box, we need to first find the radius of the soap.
The formula for the surface area of a sphere is given by:
Surface Area = 4πr^2
where r is the radius of the sphere.
Given that the surface area of the soap is 63.585 in^2 and using 3.14 as the value of pi, we can solve for r:
63.585 = 4 * 3.14 * r^2
Dividing both sides by 4 * 3.14 gives:
r^2 = 63.585 / (4 * 3.14)
r^2 = 5.1
Taking the square root of both sides gives:
r = √5.1
r ≈ 2.26
Since the radius of the soap is approximately 2.26 inches, the dimensions of the cube box should be approximately 2.26 inches in all directions.
Therefore, the correct answer is:
2.25 in. × 2.25 in. × 2.25 in.