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The total surface area of a solid cylinder is 462 $cm 2$ . The curved surface area will be one-third of its total surface area. Then what will be the radius and height of the cylinder?

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r=6cm, h=3.5cm

r=7cm, h=3.5m

r=7cm, h=3cm

r=6cm, h=3cm

answer is B.

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Detailed Solution

Given that,
The total surface area of a solid cylinder =

462 c m 2

.
The total surface area of a right cylinder =

2 π r (r + h)

.
The curved surface area = one-third of its total surface area.
Considering the total surface area as,

2 π r (r + h) = 2 π r 2 + 2 π r h

Here,

2 π r h

=the curved surface area.
We have the curved surface area of the solid cylinder as

13

of the total surface area,

⇒

= 13 × 462 = 154 c m 2

Considering the total surface area of the cylinder,

= 2 π r 2 + 2 π r h

⇒ 462 = 2 π r 2 + 154 ⇒ 462 − 154 = 2 π r 2

⇒ 308 = 2 × 227 × r 2 ⇒ 154 = 227 × r 2

⇒ 49 = r 2 ⇒ r = 7 c m

The curved surface area of the solid cylinder,

⇒ 154 = 2 π r h ⇒ 154 = 2 × 227 × 7 × h ⇒ h = 72 c m = 3.5 c m .

Thus, the radius

r = 7 c m

and the height

h = 3.5 c m

.
Therefore, the correct option is 2.

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