Marcus is making spherical soaps to sell in his online store. The surface area of the soap is 63.585 in.2 and he wants to package them into a cube box so that it fits snugly. using 3.14
if you want to fit 1 sphere in a box
4 pi R^2 = 63.585
R*2 = (63.585 / 3.14 ) /4 = 5.0625
R = 2.25
so diameter D =4.50 inches
so 4.5 * 4.5 * 4.5 fits sphere into cube
Apologies for the confusion earlier. You are correct.
If the surface area of a spherical soap is 63.585 in^2, we can solve for the radius (R) using the formula for the surface area of a sphere: 4πR^2 = 63.585.
R^2 = 63.585 / (4π) ≈ 5.0625.
Taking the square root, we get R ≈ √5.0625 ≈ 2.25.
The diameter (D) of the sphere is twice the radius, so D = 2 * 2.25 = 4.5 inches.
Hence, the soap with a diameter of 4.5 inches can fit snugly into a cube box with dimensions of 4.5 inches x 4.5 inches x 4.5 inches.
Wait so 4.5 x 4.5 x 4.5 is right?
Whew :)
I'm glad we were able to figure it out! If you have any more questions, feel free to ask.
Yes, that's correct! The appropriate cube box size to fit the soap snugly would be 4.5 inches x 4.5 inches x 4.5 inches.
To find the side length of the cube box, we need to calculate the surface area of the cube.
Since a cube has six equal square faces, its total surface area can be calculated using the formula: surface area = 6 * side^2.
Let's denote the side length of the cube as "s".
The surface area of the cube is given as 63.585 in^2.
Therefore, we have 63.585 in^2 = 6 * s^2.
Divide both sides of the equation by 6 to isolate s^2: s^2 = 63.585 in^2 / 6.
s^2 = 10.5975 in^2.
Now, take the square root of both sides to solve for s: s ≈ √10.5975 in^2.
Using a calculator, we find that s ≈ 3.26 in (rounded to two decimal places).
Therefore, the side length of the cube box should be approximately 3.26 inches.
The only answers are:
4 in x 4 in x 4 in
4.5 x 4.5 x 4.5
1.2 x 1.2 x 1.2
and 2.25 x 2.25 x 2.25
Apologies for the mistake in the previous response. Given the available options, we need to calculate the surface area of the cube for each option and compare it to the given surface area of the soap (63.585 in^2).
Option 1: 4 in x 4 in x 4 in
The surface area of a cube with side length 4 inches is 6 * (4 in)^2 = 96 in^2.
Option 2: 4.5 in x 4.5 in x 4.5 in
The surface area of a cube with side length 4.5 inches is 6 * (4.5 in)^2 = 121.5 in^2.
Option 3: 1.2 in x 1.2 in x 1.2 in
The surface area of a cube with side length 1.2 inches is 6 * (1.2 in)^2 = 8.64 in^2.
Option 4: 2.25 in x 2.25 in x 2.25 in
The surface area of a cube with side length 2.25 inches is 6 * (2.25 in)^2 = 30.375 in^2.
None of the available options match the given surface area of the soap (63.585 in^2). It seems there might be an error in the available options, or the correct packaging size is not among them.