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13 Apr 2020, 04:38
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
54% (03:15) correct
46%
(03:02)
wrong
based on 74
sessions
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A man makes complete use of 405 cubic centimetres of iron, 783 cubic centimetres of aluminium, and 351 cubic centimetres of copper to make a number of solid right circular cylinders of each type of metal. These cylinders have the same volume and each of these has radius 3 cm. If the total number of cylinders is to be kept at a minimum, then what is the total surface area of all these cylinders, in square centimetres?
A. \(846π\)
B. \(928π\)
C. \(1026(1 + π)\)
D. \(1044(4 + π)\)
E. \(1044(5 + π)\)
Are You Up For the Challenge: 700 Level Questions
A. \(846π\)
B. \(928π\)
C. \(1026(1 + π)\)
D. \(1044(4 + π)\)
E. \(1044(5 + π)\)
Are You Up For the Challenge: 700 Level Questions
Updated on: 18 Jun 2024, 08:25
Originally posted by GMATinsight on 13 Apr 2020, 05:08.
Last edited by Bunuel on 18 Jun 2024, 08:25, edited 3 times in total.
Last edited by Bunuel on 18 Jun 2024, 08:25, edited 3 times in total.
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Bunuel
Volume of Cylinder = Common Divisor of volumes {405, 783, 351} = 27
i.e. Volume of cylinder \(= πr^2*h = 27\)
i.e. Height = 3/π
i.e. Number of iron cylinders = 405/27 = 15
i.e. Number of Al cylinders = 783/27 = 29
i.e. Number of Cu cylinders = 351/27 = 13
Total Cylinders = 57
Surface Area of Cylinder \(= 2πr^2+2πrh = 2πr(r+h)\)
Surface area of 57 cylinders \(= 57*2*3(3π+3π/π) = 1026(π+1) \)
Answer: Option C
General Discussion
13 Apr 2020, 05:10
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Volume of 1 cylinder = GCD (405,783,351) = 27
\(π r^2h = 27\)
\(h= \frac{3}{π}\)
Total number of cylinders = \([\frac{405}{27}]+[\frac{783}{27}] + [\frac{351}{27}] = 15+29+13 = 57\)
Total SA of 1 cylinder= \(2πrh+2πr^2 = 2π*3*\frac{3}{π} + 2π*9 = 18(1+π)\)
Total SA of all the cylinder = \(57*18(1+π)\) = \(1026(1 + π)\)
\(π r^2h = 27\)
\(h= \frac{3}{π}\)
Total number of cylinders = \([\frac{405}{27}]+[\frac{783}{27}] + [\frac{351}{27}] = 15+29+13 = 57\)
Total SA of 1 cylinder= \(2πrh+2πr^2 = 2π*3*\frac{3}{π} + 2π*9 = 18(1+π)\)
Total SA of all the cylinder = \(57*18(1+π)\) = \(1026(1 + π)\)
GMATinsight
