SOLUTION: A building has a square based pyramid. The building is washed by using one gallon of cleaing solution for each 250 square metersof surface. How much cleaing solution is needed to w

Question 162643This question is from textbook
: A building has a square based pyramid. The building is washed by using one gallon of cleaing solution for each 250 square metersof surface. How much cleaing solution is needed to wash the building if an edge of the square base is 96 meters and the height (not the height of the sloping face) is 220meters? This question is from textbook

Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Ok, here's the plan (strategy)!
We need to find the area of each of the four congruent isosceles triangular faces. To do this we need to find the slant-height of each face, so let's do this first:
The slant-height is represented by the hypotenuse of the right triangle formed by the height of the pyramid (220 m.) and the base which is exactly half the length of one side of the square base of the pyramid (48 m.).
We'll use the Pythagorean theorem to find the length of the slant-height (hypotenuse)" where:
c = the slant-height.
a = the length of the base of the right triangle (48 m.).
b = the height of the pyramid (220 m.).

Approx.
Now we can find the area of one of the buliding's triangular faces.
The base of the triangle here would be the length of one side of the square base of the building (96 m.), and the height of course is the slant-height just calculated (225 m.).

sq. meters.
To find the area of the four faces of the building, multiply by 4.

sq.meters.
Now for each 250 sq.meters of building surface, we need 1 gallon of cleaning solution, so we'll divide the toal surface area (43200 sq.m.) by 250.
Rounding to the nearest gallon, we get 173 gallons of cleaning solution.

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