The dimensions

The dimensions of a rectangular piece of paper are 22 cm × 14 cm. It is rolled once across the breadth and once across the length to form right circular cylinders of biggest possible surface area. Find the difference in volumes of the two cylinders that will be formed.

Correct answer:

d =  49.0197 cm³

Step-by-step explanation:

$$\begin{gathered} a=22\text{cm} \\ b=14\text{cm} \\ o=2\pi r \\ V=\pi r^{2}h \\ {r}_1=\frac{a}{2\pi }=\frac{22}{2\cdot 3.1416}\doteq 3.5014\text{cm} \\ {r}_2=\frac{b}{2\pi }=\frac{14}{2\cdot 3.1416}\doteq 2.2282\text{cm} \\ {h}_1=b=14\text{cm} \\ {h}_2=a=22\text{cm} \\ {V}_1=\pi \cdot (r_1/2{)}^2\cdot h_1=3.1416\cdot (3.5014/2{)}^2\cdot 14\doteq 134.8042{\text{cm}}^3 \\ {V}_2=\pi \cdot (r_2/2{)}^2\cdot h_2=3.1416\cdot (2.2282/2{)}^2\cdot 22\doteq 85.7845{\text{cm}}^3 \\ d=|V_2-V_1|=|85.7845-134.8042|=49.0197{\text{cm}}^3 \end{gathered}$$

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