A hollow box 10x10in with a thickness of 1in with a length of 500
Would the area be (10*10)
Would the volume be ((10*10)-(9*9))*500
the volume is the volume outside the box, less the volume inside the box.
Assuming you are given the outside dimensions, and the box has no open sides, then the interior volume would be
(10)(10)(500) - (10-2)(10-2)(100-2)
You do the same for the area. Each interior face has the 1" thickness subtracted on each side.
It occurs to me that I gave you the volume of the box's material. The interior volume is just (10-2)(10-2)(100-2)
To find the area of the hollow box, you need to determine the surface area of the outer box and subtract the surface area of the inner box.
The outer box has dimensions of 10x10 inches, so its surface area is calculated by multiplying the length and width:
Outer box surface area = 10 inches * 10 inches = 100 square inches
The inner box has dimensions of (10-2) x (10-2) inches, as the thickness on each side is 1 inch.
Inner box surface area = 8 inches * 8 inches = 64 square inches
Now, subtracting the inner box surface area from the outer box surface area gives you the area of the hollow box:
Area of the hollow box = Outer box surface area - Inner box surface area
Area of the hollow box = 100 square inches - 64 square inches
Area of the hollow box = 36 square inches
Next, let's calculate the volume of the hollow box. The volume of a box is calculated by multiplying the length, width, and height. In this case, the height is the length which is given as 500.
Volume of the hollow box = Area of the hollow box * Length
Volume of the hollow box = 36 square inches * 500 inches
Volume of the hollow box = 18,000 cubic inches