A tent is in the shape of a cylinder surmounted by a cone The diameter of the cylindrical portion is 24 m and height is 11 m.If the vertex of the cone is 16m above the ground,find the area of the canvas uesd to make the tent.
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Answer:
The area of the Canvas required for the tent is 1320 cm² .
Step-by-step explanation:
Given :
Diameter of a right circular cylinder = 24 m
Radius of a right circular cylinder, r = 24/2 = 12 cm
Height of the cylindrical portion , H = 11 m
Height of a tent = 16 m
Height of a cone, h = 16 - 11 = 5 m
Radius of a cone = Radius of a cylinder = 12 cm
Slant height of a cone, l = √r² + h²
l = √12² + 5² = √144 + 25 = √169
l = √169
l = 13 cm
Slant height of a cone, l = 13 cm
Surface area of the tent , S = curved surface area of a cylinder + curved surface area of a cone
S = 2πrH + πrl
S = πr(2H + l)
S = 22/7 × 12(2 × 11 + 13)
S = 22/7 × 12(22 + 13)
S = 22/7 × 12 × 35
S = 22 × 12 × 5
S = 1320 cm²
Hence, the area of the Canvas required for the tent is 1320 cm² .
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Answer:
Area of canvas required=πrl+2πrH
⇒πr
r
2
+h
2
+2πrH=πr(
r
2
+h
2
+2H)
=
7
22
×12(
12
2
+5
2
+2×11)=1320m
2
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