Question

A Solid Cylinder has total surface area of 462cm^2.Its curved surface area is one-third of its total surface area.Find the radius and height of the cylinder ?​

Answer 1

Given that, total surface area if cylinder is 462 cm².

Also given that, it's curved surface area is one-third of its total surface area.

Curved surface area = (Total surface area)/3

⇒ C.S.A. = 462/3

⇒ C.S.A. = 154 cm²

Now,

Curved surface area = 154 cm² = 2πrh

Total surface area = 462 cm² = 2πr(r + h)

Divide C.S.A. by T.S.A.

⇒ (2πrh)/[2πr(r+h) = 154/462

⇒ h/(r + h) = 1/3

Cross-multiply them

⇒ 3h = r + h

⇒ 2h = r

⇒ h = r/2

Now, Area of two circles = 462 - 154 = 308 cm²

Area of two circles = 2πr² = 308

⇒ 2πr² = 308

⇒ 2 × 22/7 × r² = 308

On solving we get,

⇒ r = 7 cm

So,

⇒ h = 7/2 cm = 3.5 cm

Therefore,

Radius of the cylinder is 7 cm and height is 3.5 cm.

Answer 2

$\bold\green{ANSWER=>R=7,H=3.5}$

☆GIVEN☆

• T.S.A OF CYLINDER=462cm²
• C.S.A OF CYLINDER=1/3 OF T.S.A

☆FIND☆

• RADIUS AND HEIGHT OF CYLINDER☆

☆According to the above information☆

• C.S.A=1/3*462
• C.S.A=154cm²

☆NOW, APPLYING FORMULA HERE☆

• CAS+2πr²=TSA
• 154+2πr²=462
• 2πr²=462-154
• πr²=308/2
• 22/7*r²=154
• r²=√49
• r=7cm

☆TO FIND HEIGHT APPLY THE FORMULA OF CSA☆

• CSA=2πrh
• 154=2*22/7*7*h
• h=7/2
• h=3.5cm

☆HENCE☆

• RADIUS=7cm
• HEIGHT=3.5cm