Lesson 21
Scaling One Dimension
Let’s see how changing one dimension changes the volume of a shape.
Problem 1
A cylinder has a volume of \(48 \pi\) cm^{3} and height \(h\). Complete this table for volume of cylinders with the same radius but different heights.
height (cm)  volume (cm^{3}) 

\(h\)  \(48\pi\) 
\(2h\)  
\(5h\)  
\(\frac h2\)  
\(\frac h5\) 
Problem 2
A cylinder has a radius of 3 cm and a height of 5 cm.
 What is the volume of the cylinder?
 What is the volume of the cylinder when its height is tripled?
 What is the volume of the cylinder when its height is halved?
Problem 3
A graduated cylinder that is 24 cm tall can hold 1 L of water. What is the radius of the cylinder? What is the height of the 500 ml mark? The 250 ml mark? Recall that 1 liter (L) is equal to 1000 milliliters (ml), and that 1 liter (L) is equal to 1,000 cm^{3}.
Problem 4
An ice cream shop offers two ice cream cones. The waffle cone holds 12 ounces and is 5 inches tall. The sugar cone also holds 12 ounces and is 8 inches tall. Which cone has a larger radius?
Problem 5
A 6 oz paper cup is shaped like a cone with a diameter of 4 inches. How many ounces of water will a plastic cylindrical cup with a diameter of 4 inches hold if it is the same height as the paper cup?
Problem 6
Lin’s smart phone was fully charged when she started school at 8:00 a.m. At 9:20 a.m., it was 90% charged, and at noon, it was 72% charged.

When do you think her battery will die?

Is battery life a function of time? If yes, is it a linear function? Explain your reasoning.