Exercise 9 Page 436

We want to determine the height of two cone-shaped funnels. We are given the diameter and the volume of the two cones.

We will calculate the heights of the funnels one at a time. Let's start with the small funnel!

Small Funnel

First, we need to convert the measurements to the same unit. We can convert the volume from pint to cubic inches using the given conversion factor, 1 pint is equal to 28.875 cubic inches. Let's do this! 0.5 pt * 28.875in^3/1 pt = 14.4375 in^3Next, we want to divide the diameter of the base of the cone by 2 to get the radius. d/2=r ⇒ 4.5/2= 2.25 Now, we will use the formula for the volume of a cone. V=1/3π r^2 h We substitute 14.4375 for V and 2.25 for r into the formula and solve for h.

V=1/3π r^2

SubstituteII

V= 14.4375, r= 2.25

14.4375=1/3π ( 2.25)^2 h

▼

Solve for h

CalcPow

Calculate power

14.4375=1/3π (5.0625) h

MoveRightFacToNumOne

1/b* a = a/b

14.4375=π (5.0625) h/3

MultEqn

LHS * 3=RHS* 3

43.3125=π (5.0625) h

DivEqn

.LHS /π (5.0625).=.RHS /π (5.0625).

43.3125/π (5.0625)=h

RearrangeEqn

Rearrange equation

h=43.3125/5.0625π

UseCalc

Use a calculator

h=2.723317 ...

RoundDec

Round to 1 decimal place(s)

V≈ 2.7

The height of the small funnel is about 2.7 inches.

Big Funnel

We follow the same steps for the big funnel. First, we convert the volume to cubic inches. 1 pt * 28.875in^3/1 pt = 28.875 in^3 Next, we find the radius. d/2=r ⇒ 6/2= 3 Finally, we substitute 28.875 for V and 3 for r into the formula for the volume of a cone and solve for h.

V=1/3π r^2

SubstituteII

V= 28.875, r= 3

28.875=1/3π ( 3)^2 h

▼

Solve for h

CalcPow

Calculate power

28.875=1/3π (9) h

MoveRightFacToNumOne

1/b* a = a/b

28.875=π (9) h/3