By approximation, Jude's calculation is correct and the correct option is; Yes, his calculations are correct and the volumes are equal
The given parameters are;
The length of the edges of the square pyramid, s = 9.7 inches
The height of the square pyramid, h = 9 inches
The radius of the cylinder, r = 5.47 inches
The height of the cylinder, h = 3 inches
The volume of a pyramid, [tex]\mathbf{V_{pyramid}}[/tex] = (1/3) × Base Area, B × Height, h
∴ [tex]\mathbf{V_{pyramid}}[/tex] = (1/3) × B × h
The volume of a cylinder, [tex]\mathbf{V_{cylinder}}[/tex] = Base Area, B × Height, h
Base Area, B, of a cylinder = π·r²
Therefore;
The volume of a cylinder, [tex]\mathbf{V_{cylinder}}[/tex] = π·r² × h = π·r²·h
Jude's calculations are presented as follows;
[tex]\begin{array}{lcl}Volume \ of \ Square \ Pyramid&&Volume \ of \ Cylinder\\V = \dfrac{1}{3} \cdot B\cdot (h)&&V = \pi \cdot r^2 \cdot h\\\\B = 9.7^2 = 94.09 && r^2 = 5.47^2 = 29.9209\\\\V = \dfrac{1}{3} \cdot (94.09)\cdot (9)&&V = \pi \cdot (5.47^2) \cdot (3)\\\\V= \dfrac{1}{3} \cdot (846.81)&&V = \pi \cdot (29.9209) \cdot (3)\\\\V \approx 282 \ in.^3&&V \approx 282 \ in^3\end{array}[/tex]
[tex]\mathbf{V_{pyramid}}[/tex] = (1/3) × B × h = (1/3) × s² × h
Therefore;
[tex]\mathbf{V_{pyramid}}[/tex] = (1/3) × 9.7² × 9 = 282.27
[tex]\mathbf{V_{pyramid}}[/tex] ≈ 282 in.³
[tex]\mathbf{V_{cylinder}}[/tex] = π·r²·h
Therefore;
[tex]\mathbf{V_{cylinder}}[/tex] = π × 5.47² × 3 ≈ 281.9978 ≈ 282
[tex]\mathbf{V_{cylinder}}[/tex] ≈ 282 in.³
Therefore, Jude's calculation is correct by approximation, and the volumes of the cylinder and the pyramid are approximately equal
Learn more about volumes of cylinder and pyramids here;
https://brainly.com/question/3554694
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