a solid cylinder has total surface area of 465cm sq . if curved surface area is one third of its total surface area . find the radius and height of the cylinder
Answers
Answer:-
Given:
- Total Surface Area of cylinder = 465cm²
- Curved surface area of cylinder = ⅓ of T.S.A.
To Find:
- Radius of cylinder (r)
- Height of cylinder (h)
Solution:
➥ Finding C.S.A. of cylinder
As given,
C.S.A. of cylinder = ⅓ of T.S.A.
= ⅓ × 465
= 465 ÷ 3
= 155 cm²
➥ Finding radius of cylinder
According to given condition;
T.S.A. of cylinder = 465cm²
➨ C.S.A. + area of 2 base = 465cm²
➨ 155 + 2πr² = 465 cm²
➨ 2πr² = 465 - 155
➨ πr² = 310 ÷ 2
➨ r² = (155×7)÷22
➨ r = √49.318181...
∴ radius = 7.02cm(approx.)
➥ Finding height of cylinder
C.S.A. of cylinder = 155cm²
➨ 2πrh = 155
➨ 2π7h = 155
➨ 14πh = 155
➨ π × h = 155 ÷ 14
➨ h = (11.07×7)÷22
➨ h = 77.49 ÷ 22
➨ h = 3.5222727..
∴ height = 3.52cm(approx.)
Hence,
Height = 3.52cm.
Radius = 7.02cm.
Formula to be remembered:-
▪︎C.S.A. of cylinder = 2πrh
▪︎T.S.A. of cylinder = 2πrh + 2πr² = 2πr(h+r)
▪︎Volume of cylinder = πr²h
We have,
Curved surface area
=
3
1
×
Total surface area
⇒ 2πrh=
3
1
× (2πrh+ 2πr
2
)
⇒ 4πrh= 2πr
2
⇒2h=r…(1)
Now, Total surface area
=
462
⇒ Curved surface area
=
3
1
×
462
⇒ 2πrh= 154
⇒ 2×
7
22
× 2h
2
= 154
⇒
h 2
2×22×2
154×7
=
4
49
⇒ h=
2
7
cm.
From (1) ,
r=
7