the height of a cylinder is 4 cm and the area of its base is 25πcm². what will the volume of the cylinder be plz answer correct plz
Answers
Step-by-step explanation:
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 .
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