area of curved surface of a cylinder is 4400 CM square and the circumference of its base is 110 CM find height of the cylinder and the volume of the cylinder
Answers
Given : area of curved surface of a cylinder is 4400 cm² and the circumference of its base is 110 cm
To Find : height of the cylinder and the volume of the cylinder
Solution:
R = Radius of base of cylinder
H = Height of cylinder
circumference of base of cylinder = 2πR
2πR = 110
area of curved surface of a cylinder = 2πRH
2πRH = 4400
=> 110H = 4400
=> H = 40
height of the cylinder = 40 cm
2πR = 110
=> R = 55/π
volume of the cylinder = πR²H
= 2πRH . R/2
= 4400 (55/π)/2
= 2200 * 55 /π
π = 22/7
= 100 * 55 * 7
= 38,500 cm³
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The height of the cylinder is 40 cm.
The volume of the cylinder is 38500 cm³.
Step-by-step-explanation:
We have given that,
Curved surface area of cylinder = 4400 cm²
Circumference of base = 110 cm
We have to find the height and volume of the cylinder.
Now, we know that,
Circumference of circular base = 2 π r
⇒ 110 = 2 * ( 22 / 7 ) * r
⇒ r = ( 110 * 7 ) / ( 22 * 2 )
⇒ r = 110 ÷ 22 * 7 / 2
⇒ r = ( 5 * 7 ) / 2
⇒r = 35 ÷ 2
⇒ r = 17.5
Now, we know that,
Curved surface area of cylinder = 2 π r h
⇒ 4400 = ( 2 π r ) * h
⇒ 4400 = 110 * h
⇒ h = 4400 / 110
⇒ h = 440 / 11
⇒ h = 40 cm
∴ The height of the cylinder is 40 cm.
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Now, we know that,
Volume of cylinder = π r² h
⇒ Volume of cylinder = ( 22 / 7 ) * 17.5 * 17.5 * 40
⇒ Volume of cylinder = 22 * 17.5 ÷ 7 * 17.5 * 40
⇒ Volume of cylinder = 22 * 2.5 * 700
⇒ Volume of cylinder = 55 * 700
⇒ Volume of cylinder = 38500 cm³
∴ The volume of the cylinder is 38500 cm³.