Question 936259: In Egypt four square pyramids. The main pyramid is the tallest, while the other three pyramids each is half of its height. All four pyramids must have a height to base length ratio of 2:3. A maximum amount of 30 million cubic feet of stone allocated for construction.
Question: Find the largest possible values for the base length and height, to the nearest foot , as well as the volume of each pyramid ,in scientific notation to 3 Decimal places. (volume of pyramid is V= 1/3 Bh ,where B is the area of the base and h is the height.
Main Pyramid: Smaller Pyramid:
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Base length: … base length: …
Height: … height: …
Volume: … volume : …
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! Firstly let us write the data given
Tallest pyramid
height = h
base = b
h/b = 2/3
b=(3/2) h
Volume of this pyramid= 1/3 * (3/2*h)^2*h
=1/3 * 9/4h^3
=(3/4)h^3
Volume of smaller pyramid
height = h/2
(h/2)/b = 2/3
b= (3h/4)
V= 1/3 * (3h/4)^2*(h/2)
=1/3 * 9h^2/16 *h/2
=3h^3/32
Vol of 3 pyramids = 3*3h^3/32= 9h^3/32
Sum of volumes = 30 million cu.ft
(3h^3/4) +(3h^3/32)= 3*10^7 cu.ft
multiply equation by 32
24h^3+3h^3= 32*3*10^7
27h^3= 96*10^7
h^3= 96/27 *10^7
h=328.82
base = 1.5*328.82=493.24 feet
Smaller pyramid
height = h/2 = 328.82/2=164.4 feet
base = 1.5 * 164.4=246.6 feet
apply formula and find individual volmes
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