A skilled carpenter decided to craft a special rolling pin for the local baker. He carefully joined three cylindrical pieces of wood — two small ones on the ends and one larger in the centre — to create a perfect tool. The baker loved the rolling pin, as it rolled out the smoothest dough for breads and pastries.
The length of the bigger cylindrical part is 12 cm and diameter is 7 cm and the length of each smaller cylindrical part is 5 cm and diameter is 2·1 cm.
Generated by claude-sonnet-4-6 · 2026-06-15 10:33 · grounding stimulus
Model Answer
Given:
- Bigger cylinder: length (h) = 12 cm, diameter = 7 cm → radius (R) = 3.5 cm
- Smaller cylinder: length (h) = 5 cm, diameter = 2.1 cm → radius (r) = 1.05 cm
---
(i) Volume of bigger cylindrical part:
$$V = \pi R^2 h = \frac{22}{7} \times (3.5)^2 \times 12 = \frac{22}{7} \times 12.25 \times 12 = 462 \text{ cm}^3$$
---
(ii) Curved Surface Area of bigger cylindrical part:
$$\text{CSA} = 2\pi R h = 2 \times \frac{22}{7} \times 3.5 \times 12 = 264 \text{ cm}^2$$
---
(iii) Ratio of volume of bigger part to total volume of two smaller parts:
Volume of one smaller cylinder $= \pi r^2 h = \frac{22}{7} \times (1.05)^2 \times 5 = \frac{22}{7} \times 1.1025 \times 5 = 17.325 \text{ cm}^3$
Total volume of two smaller cylinders $= 2 \times 17.325 = 34.65 \text{ cm}^3$
$$\text{Ratio} = \frac{462}{34.65} = \frac{46200}{3465} = \frac{40}{3}$$
$$\boxed{\text{Required ratio} = 40 : 3}$$
Source: Surface Areas and Volumes, CBSE Class 10 Mathematics
---
Explanation
- Always halve the diameter to get radius before substituting into formulae.
- Use $\pi = \frac{22}{7}$ unless told otherwise; it simplifies cleanly here.
- For CSA, use $2\pi rh$ (not total surface area, which includes circular ends).
- For the ratio in part (iii), compute total volume of both smaller cylinders combined, then simplify the ratio fully — examiners expect the final simplified form (40:3).