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?
Mathematics · High School · Tue Nov 03 2020
Answered on
Given :
Length = 51 cm
Width = 39 cm
Height = 28 cm
Formula :
volume of rectangular prism = L × W × H
The volume of the full tank = 51 * 39 * 28
= 55692 cm^3
And 95% of this =55692 cm^3/100 × 95
= 52907.4 cm^3
So.....the difference between the amount of water required left to fill the tank = 55692 cm^3 - 52907.4 cm^3
= 2784.6 cm^3 (1)
Volume of cylinder = πr²h
The volume of the log = (3.14) (5)^2 (44)
= 3454 cm^3 (2)
So....the volume of water that spills out of the tank is = (2) - (1)
= 3454 - 2784.6
= 669.4 cm^3
So 669.4 cm³ water spills out of tank