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…

(i) Volume of the bigger cylindrical part \(\displaystyle =\frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} \times 12\) \[=462 \mathrm{~cm}^{3} \]

(ii) The Curved Surface Area of bigger cylindrical part \(\displaystyle =2 \times \frac{22}{7} \times \frac{7}{2} \times 12\) \[=264 \mathrm{~cm}^{2} \]

(iii) (a) Total volume of the two smaller cylindrical parts \(\displaystyle =2 \times \frac{22}{7} \times \frac{2.1}{2} \times \frac{2.1}{2} \times 5\) \[=34.65 \mathrm{~cm}^{3} \] \[\text { Required ratio }=\frac{462}{34.65}=\frac{3080}{231} \] \(\displaystyle \therefore\) Required ratio is \(\displaystyle 3080: 231\)

(iii) (b) The Sum of Curved Surface Area of two smaller cylindrical parts \(\displaystyle =2 \times 2 \times \frac{22}{7} \times \frac{2.1}{2} \times 5\) \[=66 \mathrm{~cm}^{2} \]