Marcus is making spherical soaps to sell in his online store the surface area of a soap is 63.585in² and he wants to package them into a cube so that it fits snugly usung 3.14 as the value of pi what should be the dimensions of the the cube box
If Marcus is making spherical soaps, the surface area of each soap can be found using the formula for the surface area of a sphere, which is:
\[ \text{Surface Area} = 4\pi r^2 \]
where \( r \) is the radius of the sphere.
Given:
\[ \text{Surface Area} = 63.585 \text{in}^2 \]
\[ \pi \approx 3.14 \]
We need to find the radius of the soap first.
\[ 63.585 \text{in}^2 = 4 \times 3.14 \times r^2 \]
\[ 63.585 \text{in}^2 = 12.56 \times r^2 \]
\[ r^2 = \frac{63.585 \text{in}^2}{12.56} \]
\[ r^2 \approx 5.062 \text{in}^2 \]
\[ r \approx \sqrt{5.062 \text{in}^2} \]
\[ r \approx 2.25 \text{in} \]
So, the radius of each spherical soap is approximately 2.25 inches.
If Marcus wants to fit each spherical soap snugly into a cube box, the diameter of the sphere must be equal to the side length of the cube, because the sphere will just touch the sides of the cube. The diameter of the sphere is twice the radius.
\[ \text{Diameter} = 2 \times r \]
\[ \text{Diameter} = 2 \times 2.25 \text{in} \]
\[ \text{Diameter} = 4.5 \text{in} \]
Therefore, the dimensions of the cube box that will snugly fit each spherical soap should be:
Height = 4.5 inches
Width = 4.5 inches
Length = 4.5 inches
Each side of the cube box should measure 4.5 inches to comfortably contain the spherical soap.