Use the answer from Part A. Be careful about the units!
C
c
Find the volume of the new funnel.
D
d
In the formula for the volume the radius is squared.
A
a
≈ 377 cm^3
B
b
≈ 8.4 seconds
C
c
≈ 14.0 seconds
D
d
See solution.
Practice makes perfect
a
The funnel has the shape of a cone. We will find its volume using the formula for the volume of a cone with a circular base area.
V=1/3π r^2h
Our funnel has a radius of 6 cm at its base and its height is 10 cm. Let's find its volume.
The volume of the funnel is approximately 377 cm^3.
b
We know from Part A that when the funnel is full it contains approximately 377 cm^3 of oil. The oil flows out of the funnel at a rate of 45 mL/s. We also are told that the conversion rate between cubic centimeters and milliliters is 1mL=1cm^3. We can use this to write the flow rate in terms of cubic centimeters.
45 mL/s = 45 cm^3/sLet's recall the relationship between flow rate and time.
Rate=Volume/Time
To find the time t it takes to empty the funnel we will substitute the corresponding values into the relationship and solve the equation.
It takes approximately 14.0 seconds to empty the funnel.
d
Let's begin by studying how the time it takes to empty the funnel depends on the volume and flow rate.
Time=Volume/Rate
Given that the flow rate is unchanged, the relationsship tells us that the larger the volume the funnel has the longer time it takes to empty it. Let's examine how the volume of the funnel depends on its radius r and height h.
V=1/3π r^2 h
In the formula, the radius is squared. The funnel in Part A has a larger height than radius. To find the volume, the lesser of these numbers is squared. For the funnel in Part C the dimensions are switched. The numbers are the same but, to find the volume, the greater of the numbers is squared. The funnel in Part C must have a larger volume so it takes longer to empty.
