Right circular cone shaped tent has a surface area of154m'and its volume is 1232 m' then area of the cloth of the tent will be (a) 240 m2(b) 230 m (c) 440 m (d) 550 m!
Answers
Answer:
hi
Step-by-step explanation:
Correct option is
C
110 m
Here, Area of the canvas = Curved surface area of the conical tent.
Since the canvas is rectangular in shape, its area is = length × width .
Curved surface area of a cone =πrl, where r is the radius of the cone and l is the slant height.
For a cone, l=
h
2
+r
2
, where l is the slant height.
Hence, l=
24
2
+7
2
⇒l=
625
⇒l=25 cm
Hence, length ×5=
7
22
×7×25
∴ length =110 m.
Therefore, option C is correct.
Answer:
(D) 550 m
Step-by-step explanation:
Given:
The volume of a conical tent is 1232 m3
Area of the base is 154 m2
Formula used:
Volume of cone = (1/3)π r2h
Area of base conical tent = πr2
Curved surface area of cone = πrl
Radius = r, Height = h, Slant height = l
Slant height(l) = √(r2 + h2)
Calculation:
Volume of cone = (1/3)π r2h
⇒ (1/3)π r2h = 1232 m3 ----(1)
Area of base conical tent = πr2
⇒ πr2 = 154 m2 ----(2)
⇒ r = √(154 × 7/22)
⇒ r = 7 m
Putting the equation (2) in equation (1),
⇒ (1/3)× 154 × h = 1232
⇒ h = 1232 × 3/154
⇒ h = 24 m
Curved surface area of cone = πrl
Slant height(l) = √(r2 + h2)
⇒ l = √(72 + 242)
⇒ l = √625
⇒ l = 25 m
Curved surface area of cone = (22/7) × 7 × 25
⇒ 550 m2
∴ Its curved surface area is 550 m2.
