2m
2m
5m
2m
Problem of the Week
Problem C and Solutions
2.5 m
4m
4m
Reach For The Top
Problem
A rectangular storage tank has a square base with sides of length 4 m and height of 5 m. The
tank is filled with water to a height of 2.5 m. A solid cube with sides 2 m is then thrown into
the tank. Does the water level reach the top of the tank? If not, how far below the top of the
tank does the water reach?
Solution 1
First calculate the volume of water in the tank using
V olume = Length × W idth × Height.
Volume of Water = 4 × 4 × 2.5
= 40 m3
The volume of the solid cube is 2 × 2 × 2 = 8 m3 . The total volume of water plus solid cube is
40 + 8 = 48 m3 .
Let x represent the height of the water in the rectangular storage tank after the cube is thrown
in.
New Volume
48
48
∴x
=
=
=
=
Length × Width × Height
4×4×x
16 × x
3m
The new water height is 3 m and the water is 5 − 3 = 2 m from the top of the tank.
Solution 2
The tank has a square base with sides of length 4 m. What would the height of a rectangular
solid with square base of length 4 m need to be if it has the same volume as the cube? Let h
be this unknown height. Then, using the formula for the volume of a rectangular solid,
4×4×h = 2×2×2
16 × h = 8
h = 0.5
Therefore, if we increase the height of water in the tank by 0.5 m, we add 8 m3 of water.
The new water height is 2.5 + 0.5 = 3 m and the water is 5 − 3 = 2 m from the top of the tank.