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04 Nov 2020, 03:15
Kudos
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
26% (03:20) correct
74%
(03:22)
wrong
based on 38
sessions
History
Date
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Not Attempted Yet
A cylindrical pencil consists of a layer of wood surrounding a solid cylinder of graphite. The radius of the pencil is 6 mm, the radius of the graphite cylinder is 2 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/cm3 and that of graphite is Rs. 2.80/cm3.
A. Rs. 7.85
B. Rs. 8.76
C. Rs. 9.36
D. Rs. 10.56
E. none of these
A. Rs. 7.85
B. Rs. 8.76
C. Rs. 9.36
D. Rs. 10.56
E. none of these
04 Nov 2020, 05:00
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Bunuel
With an Option of none of these, approximation of \(\pi\) becomes a problem. This means that we need to take the actual value of \(\pi\) = 3.14.
With this multiplication could be a problem, so we take \(\pi = \frac{22}{7}\), which is an approximation.
We have to find the cost of the wood used and the cost of graphite. For this we need to find the volumes used for each as the cost is in terms of \(cm^3\)
Radius is in mm, so conversion to cm should be done
Volume of the cylinder = \(\pi r^2 h\)
Volume of the pencil = \(\pi\) * 0.6 * 0.6 * 10 = 3.6\(\pi\) \(cm^3\)
Volume of graphite used = \(\pi\) * 0.2 * 0.2 * 10 = 0.4\(\pi\) \(cm^3\)
Cost of graphite = 0.4\(\pi\) * 2.8 = 1.12\(\pi\)
Volume of wood used = Volume of the pencil - volume of graphite = 3.6\(\pi\) - 0.4\(\pi\) = 3.2\(\pi\)
Cost of wood = 3.2\(\pi\) * 0.7 = 2.24\(\pi\)
Total Cost = 1.12\(\pi\) + 2.24\(\pi\) = 3.36\(\pi\) = \(3.36 * \frac{22}{7} = 0.48 * 22 = 10.56\)
Option D
Arun Kumar
04 Nov 2020, 11:01
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Bunuel
volume of wood =10 pi [ (.6)^2 - (.2)^2 ] = 10 * pi * .32 = 3.2 pi
volume of graphit = 10 * pi * (.2)^2 = .4 pi
total cost = pi ( 3.2 * .7 + .4 * 2.8) = pi * (2.24 + 1.12) = pi * 3.4 = 3.14 * 3.4 ~ 10.56
Answer D
