A man makes complete use of 405 cubic centimetre of iron, 783 cubic ce

Question

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

GMATinsight · Accepted Answer

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

nick1816 · Answer

Volume of 1 cylinder = GCD (405,783,351) = 27

π r^2h = 27 
 h= \frac{3}{π}

Total number of cylinders =   +  +   = 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)

eakabuah · Answer

Total volume of Iron =  405cm^3 , total volume of Aluminum =  783cm^3  and total volume of Copper =  351cm^3 
Let the number of right circular cylinders of Iron, Aluminum and Copper made be  a,b,  and  c  respectively. Let the height of each cylinder be  h .
We know that each of the circular cylinders formed from the three metals is the same.

9*\pi*h*a=405 , hence  a= \frac{45}{\pi*h}  ----- (1) 
 9*\pi*h*b=783 , hence  b= \frac{87}{\pi*h}  ----- (2) 
 9*\pi*h*c=351 , hence  c= \frac{39}{\pi*h}  ----- (3) 
The  HCF  of  45 ,  39 , and  87 = 3 . Hence  h  must be  \frac{3}{\pi}  since a, b, and c are positive integers. This implies  a=15 ,  b=29  and  c=13

When the top and bottom of the right circular cylinder are opened, the resulting solid can be opened and spread out to form a rectangle of length = the circumference of the circle with radius,  r= 3cm  and breadth  =   h=\frac{3}{\pi} 
Total surface Area  = \frac{3}{\pi}*6\pi*(a+b+c) + 2*\pi*9(a+b+c) = (18*57 + 18\pi*57)cm^2= (1026+1026\pi)cm^2 = 1026(1+\pi)cm^2

The answer is therefore C.

UkrHurricane · Answer

How to find the GCD of such big numbers quickly?

hero_with_1000_faces · Answer

Using prime factorization: Study here https://gmatclub.com/forum/factors-mult ... 96385.html

bumpbot · Answer

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A man makes complete use of 405 cubic centimetre of iron, 783 cubic ce

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A man makes complete use of 405 cubic centimetre of iron, 783 cubic ce

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