Exercise 6 Page 458

We are making smoothies and have two different glasses from which to choose. One shaped like a cone and one shaped like a cylinder.

We want to find which of the glasses holds more volume and about how much more. Let's look at the glasses one at a time and then compare their volumes.

Cone-Shaped Glass

To use the formula for the volume of a cone, we need to find the radius r of the top circle. We know that its diameter is 5 inches so we can divide it in half to find the radius. r=5/2= 2.5 in Now, we can calculate the volume of the cone-shaped glass.

V_\text{cone}=\dfrac{1}{3}\pi r^2 h

SubstituteII

r= 2.5, h= 5

V_\text{cone}=\dfrac{1}{3}\pi ({\color{#009600}{2.5}})^2 ({\color{#0000FF}{5}})

CalcPow

Calculate power

V_\text{cone}=\dfrac{1}{3}\pi (6.25) (5)

MoveRightFacToNumOne

1/b* a = a/b

V_\text{cone}=\dfrac{\pi (6.25) (5)}{3}

UseCalc

Use a calculator

V_\text{cone}=32.724923\ldots

RoundDec

Round to 1 decimal place(s)

V_\text{cone}\approx {\color{#FD9000}{32.7}} \text{ in}^3

Cylindrical Glass

To find the volume of the cylindrical glass, we once again need to find the radius r. This time we need it for calculating the volume of a cylinder. Let's divide the diameter in half to find the radius. r=3/2= 1.5 in Now, we can calculate the volume of the cylindrical glass.

V_\text{cylinder}=\pi r^2 h

SubstituteII

r= 1.5, h= 5.5

V_\text{cylinder}=\pi ({\color{#009600}{1.5}})^2 ({\color{#0000FF}{5.5}})

CalcPow

Calculate power

V_\text{cylinder}=\pi (2.25) (5.5)

UseCalc

Use a calculator

V_\text{cylinder}=38.877209\ldots

RoundDec

Round to 1 decimal place(s)

V_\text{cylinder}\approx {\color{#A800DD}{38.9}} \text{ in}^3

Comparing the Volumes

Now, we can see that the cylindrical glass holds more. \begin{gathered} {\color{#A800DD}{38.9}} > {\color{#FD9000}{32.7}} \quad \Rightarrow \quad V_\text{cylinder} > V_\text{cone} \end{gathered} We subtract the volume of the cone-shaped glass from the volume of the cylindrical glass to find how much more it holds. 38.9 - 32.7 = 6.2 in^3 The cylindrical glass holds about 6.2 cubic inches more than the cone-shaped one.

Hints

Check the answer

Cone-Shaped Glass

Cylindrical Glass

Comparing the Volumes