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An ice cream store has the pricing shown below. You want to determine the best value. The height of the cone is 4.5 in and the d

nignag [31]

Solution:

Step 1:

We will calculate the volume of ice cream in the single scoop

The volume of the ice cream will be

$\begin{gathered} V=\frac{1}{3}\pi r^2h+\frac{2}{3}\pi r^3 \\ r=\frac{2in}{2}=1in(cone) \\ h=4.5in \\ r=\frac{3in}{2}=1.5in(radius\text{ of the hemisphere\rparen} \end{gathered}$

By substituting the values, we will have

$\begin{gathered} V=\frac{1}{3}\pi r^{2}h+\frac{2}{3}\pi r^{3} \\ V=\frac{1}{3}\times\frac{22}{7}\times1^2\times4.5+\frac{2}{3}\times\frac{22}{7}\times1.5^3 \\ V=\frac{33}{7}+\frac{99}{14} \\ V=\frac{165}{14} \\ V=11.79in^3 \end{gathered}$

Step 2:

We will use the formula below to calculate the volume of the two scoops of ic cream

$\begin{gathered} V=\frac{1}{3}\pi r^2h+\frac{4}{3}\pi r^3 \\ V=\frac{1}{3}\times\frac{22}{7}\times1^2\times4.5in+\frac{4}{3}\times\frac{22}{7}\times1.5^3 \\ V=\frac{33}{7}+\frac{99}{7} \\ V=\frac{132}{7} \\ V=18.86in^3 \end{gathered}$

Step 3:

We will use the formula below to calculate the volume of the three scoops of ic cream

$\begin{gathered} V=\frac{1}{3}\pi r^2h+\frac{6}{3}\pi r^3 \\ V=\frac{1}{3}\times\frac{22}{7}\times1^2\times4.5+2\times\frac{22}{7}\times1.5^3 \\ V=\frac{33}{7}+\frac{297}{14} \\ V=\frac{363}{14} \\ V=25.93in^3 \end{gathered}$

For the first ice cream with one scoop

$\begin{gathered} 1in^3=\frac{3.50}{11.79} \\ 1in^3=\text{ \$}0.30 \end{gathered}$

For the second ice cream with two scoops

$\begin{gathered} 1in^3=\frac{4.50}{18.86} \\ 1in^3=\text{ \$}0.24 \end{gathered}$

For the third ice cream with three scoops

$\begin{gathered} 1in^3=\frac{5.50}{25.93} \\ 1in^3=\text{ \$}0.21 \end{gathered}$

Hence,

The final answer is

The triple sold at $5.50 has the best value because it has the lowest price of $0.21 per cubic inch of the ice cream

3 0

8 months ago

What is 0.278 rounded to the nearest tenth?

Goshia [24]

Answer:

0.280

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

Help please!!!!!:( Solve the equation for x. Round your answer to two decimal places. Do not include "x =" in your answer.

svet-max [94.6K]

The solution to the problem is as follows:

If you use Ln you can get rid of e.

ln(e^0.4x) = ln(0.4)

0.4x = ln(0.4)

x = (ln(0.4))/0.4

<span>x = -2.29
</span>
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

4 0

3 years ago

Read 2 more answers

Critique Reasoning James says is greater than 10. Is James correct? Explain.

Dafna1 [17]

The is answe is less than because I have to get them up

3 0

2 years ago

Use one of your new conjectures to find the lettered angles measures. R=

amm1812

Answer:

The Exterior Angle of a Triangle Formula states that the measure of an exterior angle is equal to the sum of its remote interior angles. Therefore, r + 58 = 130 which means r = 72°.

7 0

2 years ago