Answered

What mistake, if any, did Ryder make?

Given:
[tex]\[ \text{Total Volume} = 8h + \frac{1}{2} Bh \][/tex]

Calculation:
[tex]\[
\begin{array}{l}
= 5(40)(30) + \frac{1}{2}(40)(30)(95) \\
= 6,000 + 57,000 \\
= 63,000 \text{ cubic millimeters}
\end{array}
\][/tex]

A. Ryder determined the volume correctly
B. Ryder used the wrong formula for the total volume.
C. Ryder used the wrong height for the pyramid.
D. Ryder did not apply the order of operations correctly.



Answer :

GinnyAnswer
Let's go through the problem step-by-step based on the given formula:

The given formula for the total volume is:
[tex]\[ \text{Total Volume} = 5hB + \frac{1}{2}BhH \][/tex]

We are provided with the values:
- [tex]\( h = 40 \)[/tex]
- [tex]\( B = 30 \)[/tex]
- [tex]\( H = 95 \)[/tex]

We need to calculate each term separately first and then add them up.

### Step-by-Step Calculation

1. First part of the formula:
[tex]\[ 5hB = 5 \times 40 \times 30 \][/tex]
[tex]\[ = 5 \times 1200 \][/tex]
[tex]\[ = 6000 \][/tex]

2. Second part of the formula:
[tex]\[ \frac{1}{2}BhH = \frac{1}{2} \times 30 \times 40 \times 95 \][/tex]
[tex]\[ = \frac{1}{2} \times 30 \times 3800 \][/tex]
[tex]\[ = \frac{1}{2} \times 114000 \][/tex]
[tex]\[ = 57000 \][/tex]

3. Total Volume:
[tex]\[ \text{Total Volume} = 6000 + 57000 \][/tex]
[tex]\[ = 63000 \,\text{cubic millimeters} \][/tex]

### Conclusion
Ryder's calculations match the correct calculations:

[tex]\[ \text{Total Volume} = 63000 \,\text{cubic millimeters} \][/tex]

Therefore, the given answer is correct:
- Ryder determined the volume correctly