The ratio of length to width to height of a rectangular prism is 3:4:8. If the prism is 20 feet wide, what is the surface area of the prism?
3 / 4 / 8 = L / 20 / h
L/20 = 3/4 so L= 15
20/h = 4/8 so h = 40
ends = 2 (20 * 40)
top and bottom = 2 ( 20 *15)
sides = 2 (15*40)
now add
To find the surface area of a rectangular prism, we need to know its dimensions. In this case, we are given the width of the prism as 20 feet, but we need to determine the length and height.
The ratio of length to width to height is 3:4:8. This means that for every 3 units of length, there are 4 units of width and 8 units of height. Since we know the width is 20 feet, we can use this information to find the length and height.
Let's set up a proportion using the given ratio:
Length/Width = 3/4
Cross-multiplying, we get:
4 * Length = 3 * Width
Substituting the given width as 20 feet, we have:
4 * Length = 3 * 20
Simplifying, we find:
4 * Length = 60
Dividing both sides by 4, we get:
Length = 60/4 = 15 feet
Now that we know the length, we can find the height using the same ratio.
Height/Width = 8/4
Cross-multiplying, we get:
4 * Height = 8 * Width
4 * Height = 8 * 20
4 * Height = 160
Dividing both sides by 4, we find:
Height = 160/4 = 40 feet
Now that we have the dimensions of the prism (length = 15 feet, width = 20 feet, and height = 40 feet), we can calculate the surface area.
The surface area of a rectangular prism can be found using the formula:
Surface Area = 2 * (Length * Width) + 2 * (Length * Height) + 2 * (Width * Height)
Substituting the given dimensions, we have:
Surface Area = 2 * (15 * 20) + 2 * (15 * 40) + 2 * (20 * 40)
Calculating each term, we get:
Surface Area = 2 * 300 + 2 * 600 + 2 * 800
Surface Area = 600 + 1200 + 1600
Surface Area = 3400 square feet
Therefore, the surface area of the prism is 3400 square feet.