A circus tent is in the shape of cylinder surmounted by a conical top of same diameter. If their common diameter is 56 m, the height of the cylindrical part is 6 m and the total height of the tent above the ground is 27 m, find the area of the canvas used in making the tent.
Answers
Answer:
The area of the Canvas used in making the tent is 4136 m² .
Step-by-step explanation:
SOLUTION :
Given :
Total height of the tent = 27 m
Diameter of a cylinder = 56 m
Radius of cylinder and cone, r = 56/2 = 28 m
Height of a cylindrical part , h = 6 m
Height of a conical part , H = 27 - 6 = 21 m
Slant height of cone, l = √r² + H²
l =√28² + 21²
l = √784 + 441 = √1225
l = 35 m
Slant height of cone, l = 35 m
Area of the Canvas used in making the tent = curved surface area of cylinder + curved surface area of cone
= 2πrh + πrl
= πr(2h + l)
= 22/7 × 28 (2×6 + 35)
= 22 × 4 (12 + 35)
= 88 × 47 = 4136 m²
Area of the Canvas used in making the tent is 4136 m²
Hence, the area of the Canvas used in making the tent is 4136 m²
HOPE THIS ANSWER WILL HELP YOU....
Total height of tent =27 m
Height of cylindrical part = 6 m
Height of conical part =27-6=21m
slant height of cone =56/2=28 m
slant height of cone =35 m (by using formula)
AREA of canvas use=2 × pie × radius × height + pie × radius ×slant height
= pie × radius ( 2 height + slant height)
= 22/7 × 28 ( 2×6 + 35)
= 22 x 4 x 47
= 4136 m2