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.
