# help me with the similarity and congruence

• August 10th 2008, 01:31 AM
helloying
help me with the similarity and congruence
A cup is in the form of an inverted square pyramid. When the depth of the water is 10cm, the volume of the water is 187.5cm³. When
327cm³ of water is pored into the the cup, water level rises to 14cm.Find the increase in area of the water surface in the cup.Ans is 18cm²
• August 10th 2008, 03:27 AM
topsquark
Quote:

Originally Posted by helloying
A cup is in the form of an inverted square pyramid. When the depth of the water is 10cm, the volume of the water is 187.5cm³. When
327cm³ of water is pored into the the cup, water level rises to 14cm.Find the increase in area of the water surface in the cup.Ans is 18cm²

$V = \frac{1}{3}L^2h$
where L is the length of a side of the base and h is the height. So from the first pieces of information you can find L.

Now you add some volume. You know that the result is still going to be a square pyramid, so
$V + \Delta V = \frac{1}{3}L'^2 h$
where $h'= 14~cm$. You can find the new L'. Thus
$\Delta A = L'^2 - L^2$

-Dan