(a) TSA of a closed cylinder = \(2\pi r^{2} + 2\pi rh\)
= \(2\pi r (r + h)\)
\(2 \times \frac{22}{7} \times 3.5 (3.5 + h) = 209\)
\(22(3.5 + h) = 209 \implies 77 + 22h = 209\)
\(22h = 209 - 77 = 132\)
\(h = \frac{132}{22} = 6 cm\)
(b) \(< EDB = 90°\) (angle subtended at the circumference by a semi-circle)
\(\therefore < EDF = 90° - 66° = 24°\)
\(< EDF = < EBF = 24°\) (angles in the same segment)
(ii)
\(< DEB = < DBC = 57°\) (Alternate segment theorem)
\(\therefore < BGF = 180 - (57 + 24) = 180 - 81\)
\(< BGF = 99°\)