A circus tent is cylindrical up to a height of 4 m and cone above it.

1.	A circus tent is cylindrical up to a height of 4 m and cone above it. If the diameter is 105 m and its slant height of cone is 40 m., then the total area of canvas required to built the tent is ………A) 7920 m2B) 7820 m2C) 9720 m2D) 2645 m2
Answer» Correct option is: A) 7920 m² Diameter is 2r = 105m \(\therefore\) Radius = r = \(\frac {105}{2}m\) Slant height of the cone is l = 40 m. Height of cylindrical part is h = 4 m. \(\therefore\) Total area of canvas required to build the tent. = Curved surface area of cylinder + curved surface area of cone. = \(2 \pi rh + \pi rl\) = \(2 \times \frac {22}7 \times \frac {105}2 \times 4 + \frac {22}7 \times \frac {105}2 \times 40\) = 88 \(\times\) 15 + 440 \(\times\)15 = 1320 + 6600 = 7920 \(m^2\) Hence, area of required canvas is 7920 \(m^2\) Correct option is: A) 7920 m²

A circus tent is cylindrical up to a height of 4 m and cone above it. If the diameter is 105 m and its slant height of cone is 40 m., then the total area of canvas required to built the tent is ………A) 7920 m2B) 7820 m2C) 9720 m2D) 2645 m2

Answer»

Correct option is: A) 7920 m²

Diameter is 2r = 105m

\(\therefore\) Radius = r = \(\frac {105}{2}m\)

Slant height of the cone is l = 40 m.

Height of cylindrical part is h = 4 m.

\(\therefore\) Total area of canvas required to build the tent.

= Curved surface area of cylinder + curved surface area of cone.

= \(2 \pi rh + \pi rl\)

= \(2 \times \frac {22}7 \times \frac {105}2 \times 4 + \frac {22}7 \times \frac {105}2 \times 40\)

= 88 \(\times\) 15 + 440 \(\times\)15

= 1320 + 6600

= 7920 \(m^2\)

Hence, area of required canvas is 7920 \(m^2\)

Correct option is: A) 7920 m²