A fish tank, in the shape of a rectangular prism with dimensions 51 cm by 39 cm by 28 cm, is 95% filled with water. A solid log is placed into the tank, sinks to the bottom, and makes water spill out. The log is shaped like a cylinder with a radius of 5 cm and a height of 44 cm.

How much water spills out of the tank?

Use 3.14 for pi.

My answer:

The volume of the tank is 51*39*28 = 55692 cm^3.

The volume of the empty part of the tank is 5% of it, i.e. 0.05*55692 = 2784.6 cm^3.

The volume of the cylinder is = = 3454 cm^3.

Since the cylinder is fully submerged into water, the volume of water which is spilled out is 3455 - 2784.6 = __669.4 cm^3.__

Gwendolynkristine
Jun 1, 2017

#1**+2 **

The tank can hold 55692 cm^3 (1)

The volume of the log plus the volume of the water in the tank =

pi ( 5)^2 * 44 + 55692 (.95) ≈ 56363.2 cm^3 (2)

So the approximate volume that spills out = (2) - (1) ≈ 671.152 cm^3

Our answers differ probably due to rounding......but.....close enough !!!!

CPhill
Jun 1, 2017