SSC CGL Tier II 12 Jan 2017 Paper 1

Question : 64 of 100

Marks: +1, -0

The length of a side of an equilateral triangle is 8 cm. The area of the region lying between the circum circle and the incircle of the triangle is

(\Use :\π = 22 /7)

Solution:

(2)

Radius of in circle

= { a }/ { 2√ { 3 } }

cm.
Radius of circum-circle

= a/√ 3

cm.
Where a = side of triangle
∴ Required area = Area of circum-circle – area of in–circle

= \π( ( { a }/ {√ { 3 } } ) ^ { 2 } - ( { a }/ { 2 √{ 3 } } ) ^ { 2 } )

= \π( { a ^ { 2 } } /{ 3 } - { a ^ { 2 } } /{ 12 } )

= \π( { 4 a ^ { 2 } - a ^{ 2 } }/ { 12 } )

= { 3 a ^ { 2 } \π }/ { 12 } = { \π a ^ { 2 } } /{ 4 }

= { 22 }/ { 7 } ×{ 8 × 8 }/ { 4 }

= { 352 }/ { 7 } = 50 { 2 }/ { 7 }

sq. cm.

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