Congruence and Similarity - Maths

bonkysleuth SG

A cup is in the form of an inverted square pyramid. When the depth of water is 10cm, the volume of water is 187.5cm3. When x cm3 of water is poured into the cup, the water level rises to 14cm.

(a) find the value of x

(b) find the increase in the area of the water surface in the cup.

value of x is 327, but i do not know how the find the increase in area of water surface. the answer for that is 18cm2. Does water surface refer to the top layer of the water in the cone?

thanks.

eagle SG

yes the top surface area

My guess is that the answer is wrong. Perhaps the author forgot to divide the value by 1/3. I got 54cm2 as the answer, and I'm pretty sure it is correct unless some careless mistake occurs somewhere...

The formula for volume of pyramid is 1/3 * Base Area * height, where the base area in this case refers to the surface layer of the cone.

bonkysleuth SG

yes the top surface area

The formula for volume of pyramid is 1/3 * Base Area * height, where the base area in this case refers to the surface layer of the cone.

But what is the value of the surface area? It's impossible to find it from the question, can it?

weewee SG

vol=1/3 * area of base *height

187.5=1/3*area of base *10

area of base = 56.25cm2

514.5 = 1/3 *area of new base *14

area of new base = 110.25cm2

change in area = 110.25 - 56.25 = 54cm2