A square based pyramid has base sides of 230m and height of 147m. Using the same amount of material what would the height be if the base sides were 200m?
Responses (1)
"Using the same amount of material", in other words, the two pyramids have the same volume V.
The 1st pyramid has a
base side b1 = 230m
height h1 = 147m
base area A1 = (b1)^2 = 230^2 m^2 = 52900 m^2
And the formula for all cones and pyramids:
volume V = (1/3) b^2 * h = A / 3 * h
So, both pyramids have a volume of
V = 230^2 * 147 / 3 = 2,592,100 m^3.
The 2nd pyramid has a
base side b2 = 200 m
base area A2 = 40000 m^2
It*s height h2 is then
h2 = V / (A2 / 3) = 3V / A2
h2 = 3 * 2,592,100 m^3 / 40000 m^2 = 194.4075 m.