Gasoline Containers Mark Russo has two right cylindrical containers for storing gasoline. One has a diameter of 10 in. and a height of 12 in. The other has a diameter of 12 in. and a height of 10 in.
a. Which container holds the greater amount of gasoline, the taller one or the one with the greater diameter?
b. What is the difference in volume?
V = pi * r^2 * h
V = 3.14 * 5^2 * 12
V = 942 cubic inches
Find the volume of the other cylinder the same way.
http://www.mathsteacher.com.au/year9/ch14_measurement/18_cylinder/cylinder.htm
To compare the volumes of the two containers, we will use the formula for the volume of a cylinder:
Volume = π * (radius^2) * height
where π is approximately 3.14 and radius is equal to half the diameter.
Let's calculate the volumes of the two containers:
Container 1 (Diameter: 10 in, Height: 12 in):
Radius = Diameter / 2 = 10 in / 2 = 5 in
Volume = 3.14 * (5 in)^2 * 12 in = 942 in^3
Container 2 (Diameter: 12 in, Height: 10 in):
Radius = Diameter / 2 = 12 in / 2 = 6 in
Volume = 3.14 * (6 in)^2 * 10 in = 1130.4 in^3
a. In this case, the container with the greater volume is Container 2, which has a diameter of 12 inches and a height of 10 inches.
b. The difference in volume between the two containers is given by the formula: Difference in volume = Volume of Container 2 - Volume of Container 1
Difference in volume = 1130.4 in^3 - 942 in^3 = 188.4 in^3