Question:
A slab of ice 8 in × 11 in × 2 in is melted and recast into a cylinder of 8 in diameter. What is the length of the cylinder?
A slab of ice 8 in × 11 in × 2 in is melted and recast into a cylinder of 8 in diameter. What is the length of the cylinder?
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Set volumes equal when shape changes but material remains same.
Updated On: Aug 6, 2025
- 3
- 3.5
- 4
- 4.5
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The Correct Option is B
Solution and Explanation
Volume of rectangular slab:
\[
V = 8 \times 11 \times 2 = 176 \text{ in}^3
\]
Cylinder:
Diameter = 8 in \( \) Radius \( r = 4 \) in
Let height = \( h \)
Volume of cylinder:
\[
\pi r^2 h = \pi \times 4^2 \times h = 16\pi h
\]
Equating volumes:
\[
16\pi h = 176 h = \frac{176}{16\pi} = \frac{11}{\pi} \approx \frac{11}{3.14} \approx 3.5
\]
\[
\boxed{3.5 \text{ in}}
\]
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