word problem

Question

the width of a square based storage tank is 3m less than its height tge tank has a capacity of 20m square if the dimention are integer value in meters what are they

Answer 1

Capacity is volume.

 

The volume for a square based prism, (square based storage) is given by,

 

V = s²h, where s is the width of the square base and h is the height of the tank.

s = h -3 OR 

h = s + 3

 

To find the dimensions, substitute V =20 m³

20 = s²(s +3)

20 = s³ + 3s²

0  = s³ +3s² -20 , To find a value for s graph y=s³ +3s² -20

s = 2 is the only integral solution.

h = 2 + 3=5

 

The answer is the dimensions of the tank are s = 2 and h = 5

Check: 20 = 2²(5) √