SSC CGL Tier II 12 Jan 2017 Paper 1

Question : 65 of 100

Marks: +1, -0

A solid sphere of radius 3 cm is melted to form a hollow right circular cylindrical tube of length 4 cm and external radius 5 cm. The thickness of the tube is

1 cm.
9 cm.
0.6 cm.
1.5 cm.

Validate

Solution:

(1) Volume of solid sphere

= { 4 }/ { 3 } \π ( 3 ) ^ { 3 }

36\π

cu. cm.
Volume of the metal of tube

= \π ( { R } ^ { 2 } - r ^ { 2 } ) h

cu. cm.
where R = 5 cm.
r = in-radius

∴ \π( { R } ^ { 2 } - r ^ { 2 } ) h = 36 \π

⇒( 25 - r ^ { 2 } ) × 4 = 36

⇒25 - r ^ { 2 } = { 36 }/ { 4 } = 9

⇒ r ^ { 2 } = 25 - 9 = 16

⇒ r = √ { 16 } = 4 { \cm }

∴ Thickness of tube = 5 – 4 = 1 cm.

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