The radius of the cylinder is half its height and area of the inner part is 616 sq. cms. Approximately how many litres of milk can it contain?

### Concept & Contextual Geometry "Area of the inner part" of a cylindrical container designed to hold liquids usually refers to its inner Curved Surface Area (CSA), unless it specifies total surface including the base. Curved Surface Area: $$CSA = 2\pi rh$$ Volume: $$V = \pi r^2 h$$ Conversion: $1000 \text{ cm}^3 = 1 \text{ Litre}$. ### Step-by-Step Solution * **Given:** Radius ($r$) = $\frac{h}{2}$, which means $h = 2r$. CSA = 616 sq. cms. * Substitute $h$ into the CSA formula: $$2\pi r(2r) = 616$$ $$4\pi r^2 = 616$$ $$4 \times \frac{22}{7} \times r^2 = 616$$ $$\frac{88}{7} \times r^2 = 616$$ * Solve for $r^2$: $$r^2 = \frac{616 \times 7}{88} = 7 \times 7 = 49$$ * Find $r$ and $h$: $$r = 7 \text{ cm}$$ $$h = 2(7) = 14 \text{ cm}$$ * Calculate the capacity (Volume): $$V = \frac{22}{7} \times 7^2 \times 14 = 22 \times 7 \times 14 = 154 \times 14 = 2156 \text{ cm}^3$$ * Convert to litres: $$\text{Litres} = \frac{2156}{1000} = 2.156 \approx 2.2 \text{ litres}$$ ### Exam Strategy & Shortcut Recognize that substituting $h=2r$ creates a simple relationship: $4\pi r^2 = 616$. Knowing your multiples of 22 helps you quickly spot that $616 / 88 = 7$. ### Common Pitfall A student might assume "inner part" means the total internal surface area (base + curved). However, doing that calculation ($3\pi r^2 = 616$) yields a messy non-integer radius and a volume of ~1.17 litres, which doesn't fit the given options. Trusting standard container conventions (focusing on the curved wall) is key here. ### Final Answer Therefore, the correct answer is **2.2**.