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Question
The sum of the radius of base and height of a solid right circular cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 sq. cm, find the volume of the cylinder. `("use " pi=22/7)`
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Solution
Let the radius of base and height of the solid right circular cylinder be r cm and h cm, respectively.
According to the question,
r+h=37 .....(1)
Total surface area=1628 sq cm
2πr(r+h)=1628 .....(2)
From (1) and (2), we get
2πr(37)=1628
⇒ 2πr=44
`=>2xx22/7xxr=44`
`=>r=(44xx7)/(2xx22)`
⇒ r = 7 cm
Substituting the value of r in (1), we get
7+h=37
⇒ h = 30 cm
Now,
Volume of the cylinder = πr2h
`=22/7xx7xx7xx30`
=4,620 cm3
Hence, the volume of the cylinder is 4,620 cm3.
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