A circular cylinder can hold $61.6$ c.c. of water. If the height of the cylinder is $40$ cm and the outer diameter is $16$ mm, then the thickness of the material of the cylinder is

### Concept & Inner Radius of a Cylinder The amount of water a cylinder can hold refers to its internal volume (capacity). We can find the internal radius using the volume formula, and then find the thickness by subtracting the internal radius from the outer radius. $$ V = \pi \times r^2 \times h $$ $$ \text{Thickness} = \text{Outer Radius} (R) - \text{Inner Radius} (r) $$ ### Step-by-Step Solution - **Given:** - Capacity (Internal Volume) $V = 61.6$ c.c. ($1$ c.c. = $1$ cm$^3$). - Height $h = 40$ cm. - Outer diameter = $16$ mm $\implies$ Outer radius $R = 8$ mm = $0.8$ cm. - **Calculation:** - Let $r$ be the inner radius in cm. - $61.6 = \frac{22}{7} \times r^2 \times 40$ - $r^2 = \frac{61.6 \times 7}{22 \times 40}$ - $r^2 = \frac{431.2}{880}$ - To simplify, convert the decimal: $r^2 = \frac{4312}{8800} = \frac{539}{1100} = \frac{49}{100}$ - $r = \frac{7}{10} = 0.7$ cm. - Convert $r$ to mm: $0.7$ cm = $7$ mm. - Thickness = $R - r = 8$ mm - $7$ mm = $1$ mm. ### Exam Strategy & Shortcut Keep track of units carefully. Notice the volume and height are in cm, but the diameter and options are in mm. It's usually best to work in cm until the final step, then convert back. ### Common Pitfall Using the diameter instead of the radius for calculation, or forgetting to unify the units (cm vs. mm) before solving. ### Final Answer Therefore, the correct answer is **1 mm**.