The difference can be found by subtracting the volume of the smaller cylinder from the volume of the larger cylinder.
D
d
Example Solution: V_L-V_S=1.5Ï€
Practice makes perfect
a
Let's draw two cylinders where neither the radius nor the height is the same. Note, to illustrate the cylinder as a 3D solid, you need to draw an oval instead of a circle for the top and bottom.
b
Even though the drawing is only a 2D representation of a 3D solid, we can measure the height along a vertical edge. We can also measure the radius from the midpoint to the end of the longest diameter of the oval.
We can find the volume of the other cylinder similarly. Let's include a column in the table for the volumes.
Radius
Height
Volume
1in.
3in.
Ï€* 1^2*3 = 3Ï€in.^3
1.5in.
2in.
Ï€* 1.5^2*2 = 4.5Ï€in.^3
c
The difference can be found by subtracting the volume of the smaller cylinder from the volume of the larger cylinder.
d
If we call the volume of the smaller cylinder V_S and the volume of the larger cylinder V_L, then we can use subtraction to express the difference.
V_L-V_S
For the cylinders in Part A, the smaller volume is V_S=3Ï€, and the larger volume is V_L=4.5Ï€. Let's do the subtraction to find the difference.
