A circus tent is cylindrical to a height of 8 m surmounted by a conical part. If total height of the tent is 13 m and the diameter of its base is 24 m; calculate:

(i) total surface area of the tent

(ii) area of canvas, required to make this tent allowing 10% of the canvas used for folds and stitching.

Given,

Height of the cylindrical part (H) = 8 m

Height of the conical part (h) = (13 - 8) m = 5 m

Diameter of base = 24 m

From figure,

Radius of cone and cylinder are equal (r) = $\dfrac{24}{2}$ = 12 m.

By formula,

⇒ (l)² = r² + h²

⇒ l² = 12² + 5²

⇒ l² = 144 + 25

⇒ l² = 169

⇒ l = $\sqrt{169}$

⇒ l = 13 m.

(i) Total surface area of the tent = 2πrH + πrl = πr(2H + l)

= $\dfrac{22}{7}$ x 12 x (2 x 8 + 13)

= $\dfrac{264}{7}$ (16 + 13)

= $\dfrac{7656}{7}$ m²

= 1093.71 m².

Hence, total surface area of tent = 1093.71 m².

(ii) According to question,

Area of canvas used in stitching = $\dfrac{10}{100} \times$ Total area of canvas

⇒ Total area of canvas required = Total surface area of tent + Area of canvas used in stitching

⇒ Total area of canvas = $\dfrac{7656}{7} + \dfrac{1}{10}$ Total area of canvas

⇒ Total area of canvas - $\dfrac{1}{10}$ Total area of canvas = $\dfrac{7656}{7}$

⇒ $\dfrac{9}{10}$ Total area of canvas = $\dfrac{7656}{7}$

⇒ Total area of canvas = $\dfrac{7656}{7} \times \dfrac{10}{9}$

⇒ Total area of canvas = 1215.23 m².

Hence, the total area of canvas required = 1215.23 m².