A spherical container is designed to hold as much volume as the rectangular prism above it's radius is 3.7 in find the surface area of the sphere rounded to the nearest square inch
To begin solving the problem, we need to find the volume of the rectangular prism. Let's assume that the dimensions of the prism are l, w, and h. Then, the volume is given by:
V = lwh
We don't know the values of l, w, and h, but we do know that the sphere is designed to hold as much volume as the prism. This means that the volume of the sphere is equal to V:
V_sphere = V
The volume of a sphere with radius r is given by:
V_sphere = (4/3)πr^3
Substituting r = 3.7 into this formula, we get:
V_sphere = (4/3)π(3.7)^3 ≈ 202.9
Now we can solve for the dimensions of the rectangular prism:
V = lwh
202.9 = lwh
We don't know the values of l, w, and h, but we do know that the surface area of the sphere is equal to the surface area of the cylindrical container.
The surface area of a sphere with radius r is given by:
A_sphere = 4πr^2
Substituting r = 3.7 into this formula, we get:
A_sphere = 4π(3.7)^2 ≈ 171.9
So, the surface area of the spherical container is approximately 171.9 square inches. Rounded to the nearest square inch, the answer is 172 square inches.