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.

Question

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.

KnowledgeBoat · Accepted Answer

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) = = 12 m. By formula, ⇒ (l)² = r² + h² ⇒ l² = 12² + 5² ⇒ l² = 144 + 25 ⇒ l² = 169 ⇒ l = ⇒ l = 13 m. (i) Total surface area of the tent = 2πrH + πrl = πr(2H + l) = x 12 x (2 x 8 + 13) = (16 + 13) = m² = 1093.71 m². Hence, total surface area of tent = 1093.71 m². (ii) According to question, Area of canvas used in stitching = Total area of canvas ⇒ Total area of canvas required = Total surface area of tent + Area of canvas used in stitching ⇒ Total area of canvas = Total area of canvas ⇒ Total area of canvas - Total area of canvas = ⇒ Total area of canvas = ⇒ Total area of canvas = ⇒ Total area of canvas = 1215.23 m². Hence, the total area of canvas required = 1215.23 m².

Mathematics

Mensuration

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