a rectangular prism has a surface area of 432 square inches, a height of six inches, and a width of 12 inches. what is the volume?
V = LWH <----(length x width x height)
First we need to figure out the Length, since we already know the values of the Width (12 in.)and Height (6 in.).
Since we know the value of the Surface Area, we can use that equation to figure out the Length value… SA = 2(WL + HL + HW)
Let’s plug the numbers that we already know into this equation:
432 = 2(12L + 6L + (12 x 6))
432 = 2(12L + 6L + 72) <—we can add 12L plus 6L since they both have the same coefficient
432 = 2(18L + 72) <----now we can multiply everything inside the parenthesis by 2
432 = 36L + 144 <—we want to get the L value by itself on one side of the equal sign
432 - 144 = 36L <—subtract 144 from each side so the L value is by itself
288 = 36L <—to get ONLY the value of the L, we will now divide both sides by 36
8 = L
Now that we know the L=8, H=6, and W=12…we can plug those numbers into the equation for volume, which is:
V = LWH <----Length x Width x Height
V = 8 x 12 x 6
V = 576