A solid cylinder has the total surface area 231 square cm.

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A solid cylinder has the total surface area 231 square cm. If its curved surface area is 2/3 of the total surface area, then the volume of the cylinder is

Let the radius of cylinder be r cm.
Height = h cm.
According to the question,
2πrh + 2πr² = 231

Again, 2πrh =	2	× 231 = 154
	3

∴ 2πr² = 231 – 154

⇒ 2 ×	22	r² = 77
	7

⇒ r² =	77 × 7	=	49
	22 × 2		2 × 2

⇒ r =	7	cm.
	2

∴ 2πrh = 154

⇒ 2 ×	22	×	7	× h = 154
	7		2

⇒ 22h = 154

⇒ h =	154	= 7 cm.
	22

∴ Volume of cylinder = πr²h

=		22	×	7	×	7	× 7		cu.cm.
		7		2		2

= 269.5 cu. cm.