Diagram 2 shows a cylindrical vessel resting on a horizontal plane. The vessel Which
has radius 6 cm and length 20 cm, contains liquid to a depth of 9 cm. The value (in cu
em) of liquid in the vessel is :
(a) 1584
(c) 1507
(b) 1680
(d) 1820
Answers
Answer:
options d is the correct answer
Given : a cylindrical vessel resting on a horizontal plane. The vessel Which has radius 6 cm and length 20 cm, contains liquid to a depth of 9 cm
complete Question : https://brainly.in/question/37434855
To Find : Volume of liquid in vessel
(a) 1584
(c) 1507
(b) 1680
(d) 1820
Solution :
Cos ∠POB = OP/OB = 3/6 = 1/2 = Cos 60°
=> ∠POB = 60°
∠AOB = 2 ∠POB = 2 × 60° = 120°
∠AOB = 120°
Area of ΔAOB = (1/2) OA * OB Sin ∠AOB
= (1/2) * 6 * 6 * sin 120°
= 18 * √3/2
= 9√3
= 15.588
= 15.6 cm²
∠AOB = 120°
=> bigger angle = 360° - 120° = 240°
Area of bigger sector AOB = ( 240° / 360° ) π * 6²
= 24π
Volume of liquid in vessel = ( area of bigger sector AOB + area of ΔAOB ) * length
= ( 24π + 15.6 ) * 20
= 1820 cm²
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