The Inverted Pyramid as an Application of Integration | Calculus II
Here we use integration to calculate the mass of liquid in a pyramid-shaped tank.
A tank is shaped like an upside down pyramid: it is 10 meters tall, and its base is a square of side length 5. It is full to the brim with a liquid having density p = 1450 kg/m^3. Let x be the depth of the tank: it is zero at the to and 10m at the bottom.
Write down a formula for the area of the cross section A(x) as a function of depth. Write a definite integral that computes the total mass of the liquid in the tank.