SOLUTION: A rectangular pyramid has a volume of 190 cubic centimeters. Find two possible sets of measurement for the base area and height of the pyramid
Algebra.Com
Question 868327: A rectangular pyramid has a volume of 190 cubic centimeters. Find two possible sets of measurement for the base area and height of the pyramid
Found 2 solutions by Alan3354, jim_thompson5910:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Vol = L*W*H/3 = 190
Vol = BA*H/3 = 190
BA*H = 570
1*570 = 570
(pi*11)*570/(11pi) = 570
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
The volume of a pyramid is
V = (1/3)*A*h
where V is the volume, A is the area of the base, h is the height.
Plug in V = 190 and isolate A*h to get
V = (1/3)*A*h
190 = (1/3)*A*h
190*3 = A*h
570 = A*h
Now solve for either A or h. I'm going to solve for A to get
570 = A*h
570/h = A
A = 570/h
Now we can plug in arbitrary values of h to get corresponding values of A.
For example, if h = 1, then
A = 570/h
A = 570/1
A = 570
Or if h = 2, then
A = 570/h
A = 570/2
A = 285
So two possible sets of measurement for the base area A and the height h are:
A = 570, h = 1
A = 285, h = 2
There are infinitely more combos (just make sure both A and h are positive).
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