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 ->  Volume -> 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       Log On


   

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) About Me  (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) About Me  (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).