Answer:
The value of r is 13/4.
Step-by-step explanation:
As per given question we have provided that :
- >> U = 16½
- >> h = 2
- >> π = 22/7
Finding the value of r by substituting the values in the formula :
[tex]\begin{gathered} \qquad{\implies{\sf{U = \pi \Big[r + h\Big]}}}\\\\\qquad{\implies{\sf{16\frac{1}{2} = \dfrac{22}{7} \Big[r + 2\Big]}}}\\\\ \qquad{\implies{\sf{\frac{33}{2} = \dfrac{22}{7} \Big[r + 2\Big]}}}\\\\\qquad{\implies{\sf{\frac{33}{2} \times \dfrac{7}{22} = \Big[r + 2\Big]}}} \\\\\qquad{\implies{\sf{\frac{\cancel{33}}{2} \times \dfrac{7}{\cancel{22}} = \Big[r + 2\Big]}}}\\\\\qquad{\implies{\sf{\frac{3}{2} \times \dfrac{7}{2} = \Big[r + 2\Big]}}}\\\\\qquad{\implies{\sf{\frac{3 \times 7}{2 \times 2} = \Big[r + 2\Big]}}}\\\\\qquad{\implies{\sf{\frac{21}{4} = \Big[r + 2\Big]}}}\\\\\qquad{\implies{\sf{r = \dfrac{21}{4} - 2}}}\\\\\qquad{\implies{\sf{r = \dfrac{21 - 8}{4}}}}\\\\\qquad{\implies{\sf{r = \dfrac{13}{4}}}}\\\\ \qquad{\star{\underline{\boxed{\sf{r = \dfrac{13}{4}}}}}}\end{gathered}[/tex]
Hence, the value of r is 13/4.
[tex]\rule{300}{2.5}[/tex]
