Let radius \(r\), slant height \(l = 7\) m, and total canvas area \(= 77\) m² Lateral surface area \(= \pi r l = 7\pi r\) Base area \(= \pi r^2\) Total area \(= 7\pi r + \pi r^2 = 77\) \(\pi r(r + 7) = 77\) \(r(r + 7) = \frac{77}{\pi} \approx 24.52\) \(r^2 + 7r - 24.52 = 0\) \(r = \frac{-7 \pm \sqrt{147.08}}{2} \approx \frac{-7 \pm 12.13}{2}\) \(r \approx 2.565\) Base area \(= \pi r^2 \approx 3.1416 \times 6.58 \approx 20.67\) m²

Q.Let radius \(r\), slant height \(l = 7\) m, and total canvas area \(= 77\) m² Lateral surface area \(= \pi r l = 7\pi r\) Base area \(= \pi r^2\) Total area \(= 7\pi r + \pi r^2 = 77\) \(\pi r(r + 7) = 77\) \(r(r + 7) = \frac{77}{\pi} \approx 24.52\) \(r^2 + 7r - 24.52 = 0\) \(r = \frac{-7 \pm \sqrt{147.08}}{2} \approx \frac{-7 \pm 12.13}{2}\) \(r \approx 2.565\) Base area \(= \pi r^2 \approx 3.1416 \times 6.58 \approx 20.67\) m² (a) 38.5 square meters (b) 39.5 square meters (c) 36.5 square meters (d) 37.5 square meters

Answer: A

Here, curved surface area \(= \pi r l = 77\) So, \(\frac{22}{\cancel{7}} \times r \times \cancel{7} = 77\) Therefore, \(r = \frac{77}{22} = \frac{7}{2}\) \(\therefore\) Base area \(= \pi \left(\frac{7}{2}\right)^2\) square meters \(= \frac{22}{7} \times \frac{49}{4}\) square meters \(= \frac{77}{2}\) square meters \(= 38.5\) square meters