A solid cylinder has a total surface area of 231cm^2.Its curved surface area is one-third of its total surface area.Find the volume of the cylinder.
Ans.-190.54
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t.s.a of solid cylinder = 231cm^2
2πrh + 2πr^2 = 231 ----(1)
c.s. a of solid = 1/ 3rd of t.s.a
2πrh = 1 × 231/ 3 = 77 cm^2
2πrh = 77. ----(2)
from (1)
77 + 2πr^2 = 231
2πr^2 = 154 => r^2 = 154 × 7/ 2 × 22
r^2 = 24.5 => r = 4.9cm ( approx.)
put value of r in (2) , we get
2π × 4.9× h = 77
9.8 πh = 77 => h = 77 × 7/ 9.8 × 22
h = 2.5cm
volume of solid cylinder
= πr^2h = 22 × (4.9)^2 × 2.5/ 7
= 188.65cm^2 (approx.)
Answer: volume = 188.65cm^2
2πrh + 2πr^2 = 231 ----(1)
c.s. a of solid = 1/ 3rd of t.s.a
2πrh = 1 × 231/ 3 = 77 cm^2
2πrh = 77. ----(2)
from (1)
77 + 2πr^2 = 231
2πr^2 = 154 => r^2 = 154 × 7/ 2 × 22
r^2 = 24.5 => r = 4.9cm ( approx.)
put value of r in (2) , we get
2π × 4.9× h = 77
9.8 πh = 77 => h = 77 × 7/ 9.8 × 22
h = 2.5cm
volume of solid cylinder
= πr^2h = 22 × (4.9)^2 × 2.5/ 7
= 188.65cm^2 (approx.)
Answer: volume = 188.65cm^2
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