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
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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
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Answer:
Answer:
The height of the cylinder is 39.99 cm and volume of the cylinder is 38543.332 cm³ .
Step-by-step explanation:
Formula
Curved\ surface\ area\ of\ a\ cylinder = 2\pi rhCurved surface area of a cylinder=2πrh
Circumference\ of\ the\ cylinder\ base = 2\pi rCircumference of the cylinder base=2πr
Volume\ of\ the\ cylinder\ base =\pi r^{2} hVolume of the cylinder base=πr
2
h
Where r is the radius and h is the height .
As given
The curved surface area of a cylinder is 4400 cm² and the circumference of its base is 110 cm.
\pi = 3.14π=3.14
Put the values in the equation
110= 2\times 3.14\times r110=2×3.14×r
r = \frac{110}{6.28}r=
6.28
110
r = 17.52 cm (Approx)
Put in the curved surface area formula of a cylinder
4400= 2\times 3.14\times 17.52\times h4400=2×3.14×17.52×h
4400= 110.03\times h4400=110.03×h
h = \frac{4400}{110.03}h=
110.03
4400
h = 39.99 cm (Approx)
Therefore the height of the cylinder is 39.99 cm .
Put in the formula of volume of a cylinder .
Volume\ of\ the\ cylinder\ base =3.14\times 17.52\times 17.52\times 39.99Volume of the cylinder base=3.14×17.52×17.52×39.99
Volume\ of\ the\ cylinder\ base =38543.332\ cm^{3}Volume of the cylinder base=38543.332 cm
3
Therefore the height of the cylinder is 39.99 cm and volume of the cylinder is 38543.332 cm³ .
Answer:
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.