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. 3
• B. 3.5
• C. 4
• D. 4.5

Hint:

Set volumes equal when shape changes but material remains same.

Answer 1

The Correct Option is B

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: \[ 16\pi h = 176 h = \frac{176}{16\pi} = \frac{11}{\pi} \approx \frac{11}{3.14} \approx 3.5 \] \[ \boxed{3.5 \text{ in}} \]