Question

a circus tent is cylindrical up to a height of 15 m and conical above it if the diameter of the base is 56m and the total height of the 60m find the total Canvas used in making the tent​

Answer 1

Answer:

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