CAT 2016 Quantitative Ability

Question : 13 of 34

Marks: +1, -0

An unsharpened cylindrical pencil consists of a layer of wood surrounding a solid cylinder of graphite. The radius of a pencil is 7 mm, the radius of the graphite cylinder is 1 mm and the length of the pencil is 10 cm. Find the cost of the material used in a pencil, if the cost of wood is

\Rs.0.70\/\cm^3

and that of graphite is

\Rs.2.10\/\cm^3

Rs.8.76
Rs.10.02
Rs.11.22
Rs. 13.74

Validate

Solution:

Volume of a cylinder =

πr^2h

, where
r = radius of the cylinder
h = height of the cylinder
Volume of the graphite cylinder

=π( {1}/{10})^{2}×10

= {π}/{10} {cm}^{3}

Volume of the layer of wood

=10π[( {7}/{10})^{2}-( {1}/{10})^{2}]= {48π}/{10} {cm}^{3}

Cost of the material in a pencil

=\;\;{π}/{10}×2.10+\;\;{48π}/{10}×0.70

= Rs. 11.22

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