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### Multiple Choice (Worth 4 Points)

What is the volume of a square pyramid with base edges of 7 in and a height of 7 in? Is it equal to the volume of a cylinder with a radius of 7 in and a height of 7 in? Jude rounded all values to the nearest whole number. Examine Jude's calculations. Is he correct?

[tex]\[
\begin{tabular}{|l|l|}
\hline
Square Pyramid & Volume of Cylinder \\
\hline
& $V = r^2 h$ \\
\hline
& $V = (7^2)(7)$ \\
\hline
& $V = 343 \text{ in}^3$ \\
\hline
\end{tabular}
\][/tex]

A. His calculations are correct and the volumes for both figures are equal.

B. He made a mistake in solving for the volume of the square pyramid.

C. He made a mistake in solving for the volume of the cylinder.

D. He made a mistake in solving for the volume of both figures.

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### Multiple Choice (Worth 4 Points)

A chain was made from a cylinder that has a radius of 2.5 cm and a height of 22 cm. How much plastic coating would be needed to coat the surface of the chain link? Use 3.14 for π.

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### Question 1 (Answered)

[tex]$Nan =$[/tex]

[tex]$CH = -2$[/tex]



Answer :

Let's address the question step by step.

Step 1: Calculate the volume of the square pyramid.

The formula for the volume [tex]\( V \)[/tex] of a pyramid with a square base is:
[tex]\[ V = \dfrac{1}{3} \times \text{base\_area} \times \text{height} \][/tex]

Given:
- Base edge length ([tex]\( a \)[/tex]) = 7 inches
- Height ([tex]\( h \)[/tex]) = 7 inches

First, calculate the base area:
[tex]\[ \text{base\_area} = a^2 = 7^2 = 49 \, \text{square inches} \][/tex]

Next, calculate the volume:
[tex]\[ V_{\text{pyramid}} = \dfrac{1}{3} \times 49 \times 7 \approx 114.33 \, \text{cubic inches} \][/tex]

Step 2: Calculate the volume of the cylinder.

The formula for the volume [tex]\( V \)[/tex] of a cylinder is:
[tex]\[ V = \pi \times r^2 \times h \][/tex]

Given:
- Radius ([tex]\( r \)[/tex]) = 7 inches
- Height ([tex]\( h \)[/tex]) = 7 inches

Using [tex]\( \pi \approx 3.14 \)[/tex]:

First, calculate the base area:
[tex]\[ r^2 = 7^2 = 49 \][/tex]
Next, calculate the volume:
[tex]\[ V_{\text{cylinder}} = 3.14 \times 49 \times 7 \approx 1077.57 \, \text{cubic inches} \][/tex]

Step 3: Round the volume of the cylinder to the nearest whole number.

When rounded:
[tex]\[ V_{\text{cylinder}} \approx 1078 \, \text{cubic inches} \][/tex]

Step 4: Check Jude's calculations.

Jude mentioned the volume of his cylinder as 343 cubic inches. Let's compare:

- Jude's volume for the cylinder is 343 cubic inches.
- The actual calculated volume (rounded) is 1078 cubic inches.

Clearly, the correct volume of the cylinder (1078 cubic inches) does not match Jude's volume (343 cubic inches).

So, Jude made a mistake in calculating the volume of the cylinder.

Final answer to the question:

Jude made a mistake in solving for the volume of the cylinder.