the roof is a right rectangular prism and the floor is a rectangle. (its the outside of a warehouse). for the roof- the base has 51 x 51. The rectangular for the floor is 120 (l) x 20 (h) x 90 (w). need to find the volume and surface area. (counting the floor) Give an organized list for how you figured out the SA (floor= 120x90=10,800, front left=etc.) teacher said I would have to find the missing piece for the roof using the pathagorean theorem but what is the missing peice? Height maybe?
Can you tell me something? Why should "math for teachers" be any different from math for everyone? Shouldn't teachers be as well taught as everyone else?
To find the missing piece for the roof, we can use the Pythagorean theorem. In a right rectangular prism, the roof is formed by the slant height, height, and the base.
Given that the base of the roof is 51 x 51, it is a square with equal sides. Let's denote the missing piece of the roof as "h", which represents the height of the roof.
Using the Pythagorean theorem, we can set up the equation as follows:
h^2 = (51/2)^2 + (51/2)^2
= (51^2/4) + (51^2/4)
= 2(51^2/4)
= (51^2/2)
≈ 1303.25
Therefore, the height of the roof (missing piece) is approximately √1303.25 ≈ 36.1.
Now, let's calculate the volume and surface area of the right rectangular prism:
To find the volume, we multiply the length, width, and height. In this case, the dimensions are 120 (length), 90 (width), and 20 (height).
Volume = length x width x height
= 120 x 90 x 20
= 216,000 cubic units
To find the surface area, we need to consider the six faces of the right rectangular prism.
Surface area = 2lw + 2lh + 2wh + base area
= 2(120 x 90) + 2(120 x 20) + 2(90 x 20) + (120 x 90)
= 21,600 + 4,800 + 3,600 + 10,800
= 40,800 square units
Considering the floor as well, the total surface area would be 40,800 + (120 x 90) = 51,000 square units.
Thus, the volume of the right rectangular prism is 216,000 cubic units, and the surface area (including the floor) is 51,000 square units.