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# A Solid Cylinder Has Total Surface Area of 462 Cm2. Its Curved Surface Area is One-third of Its Total Surface Area. Find the Radius and Height of the Cylinder. - Mathematics

Course
ConceptSurface Area of a Right Circular Cylinder

#### Question

A solid cylinder has total surface area of 462 cm2. Its curved surface area is one-third of its total surface area. Find the radius and height of the cylinder.

#### Solution

We have
Curved surface area = 1/3 × total surface area

⇒ 2πrh = 1/3(2 πrh + 2πr^2)

⇒ 6πrh = 2πrh +2πr^2

⇒ 4πrh =2πr^2

⇒ 2h = r
We know that,
Total surface area = 462
⇒ Curved surface Are = 1/3× 462

2πrh =154

⇒ 2× 3.14× 2h^2 = 154

⇒ h^2=(154× 7)/(2× 22× 2)

⇒ 49/4

⇒ h=7/2cm

⇒ r=2h

⇒ r=2× 7/2cm

⇒ r=7cm.

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Solution for Mathematics for Class 9 by R D Sharma (2018-19 Session) (2018 to Current)
Chapter 19: Surface Areas and Volume of a Circular Cylinder
Ex. 19.1 | Q: 12 | Page no. 8

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Solution A Solid Cylinder Has Total Surface Area of 462 Cm2. Its Curved Surface Area is One-third of Its Total Surface Area. Find the Radius and Height of the Cylinder. Concept: Surface Area of a Right Circular Cylinder.
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