Consider a basketball packaged in a box that is in the shape of a cube. We are told that the edge length of the box is equal to the diameter of the basketball. This means that to find the surface area of the package, we need to find the diameter of the basketball. To do so, we can recall the formula for the volume of a sphere.
V=4/3Ï€ r^3
Here, r is the radius of the sphere. We know that the volume of the basketball is 121.5Ï€ cubic inches. Then, we can substitute V= 121.5Ï€ into the above formula and solve it for r to calculate the radius of the basketball.
The radius of the basketball is 4.5 inches. Remember that the diameter is equal to the double of the radius.
d=2r → d= 9 inches
Now that we have the diameter of the basketball we can use the formula for the surface area.
S_A = L_A + A_B
Here, L_A is the total area of all lateral surfaces. In our case the lateral surfaces are four squares and the bases are also squares, which means that we have 6 squares. Then, the surface area will be equal to the product of 6 multiplied by the area of a square.
S_A = 6s^2
Here, s is the edge length of the square. We know that the edge length is equal to the diameter of the basketball, then we can substitute s= 9 into the above formula to find the surface area of the box.
The surface area is equal to square 486 square inches. Finally, we will recall the formula for the volume of a cube.
V=s^3
Let's substitute s= 9 into the above formula to find the volume of the box.
