A circus tent is in the shape of a cylinder surmounted by a conical top of same diameter. If their common diameter is 56 cm, the height of cylindrical part is 6 m and the total height of the tent above the ground is 27 m, find the area of canvas used in making the tent.

Given:

Diameter = 56 cm = 0.56m

Height of cylindrical part = 6 m

Total Height = 27 m

∵ Diameter = 0.56 m

∴ Radius = 1/2 × 0.56 m = 0.28 m

Also,

Height of conical part = Total height – Height of cylindrical part

⇒ Height of conical part = 27 m – 6 m

⇒ Height of conical part (h) = 21 m

Clearly,

Total Surface Area of canvas = Curved surface area of cylinder + Curved surface area of cone …(1)

Curved surface area of cylinder = 2πrh

⇒ Curved surface area of cylinder = 2 × 22 × 0.04 ×6

⇒ Curved surface area of cylinder = 10.56 m²

Curved surface area of cone = πrl …(2)

(where, l = slant height)

To find l,

l² = r² + h²

⇒ l² = 0.28² + 21²

⇒ l² = 0.0784 + 441

⇒ l² = 441.0784

⇒ l = √441.0784 ~ 21

⇒ l = 21 cm

Put the value of l in (2),

⇒ Curved surface area of cone = 22 × 0.28 × 3

⇒ Curved surface area of cone = 18.48 cm²

Putting all the values in (1),

Total Surface Area of remaining solid = 10.56 cm² + 18.48 cm²

⇒ Total Surface Area of remaining solid = 29.04 cm²

Hence, Total Surface Area of canvas = 29.04 cm²