# Quantitative Aptitude – Geometry – A man makes complete use of 405 cc

## A man makes complete use of 405 cc – Video Solution

Q. A man makes complete use of 405 cc of iron, 783 cc of aluminium, and 351 cc 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 the total surface area of all these cylinders, in sq cm, is?
1. 8464π
2. 928π
3. 1026(1 + π)
4. 1044(4 + π)

Solution: As cylinders have the same volume and each of these has radius 3 cm. So volume of each cylinder will be equal to HCF of (405, 783 and 351) which is 27.
So volume of each cylinder = 27
No of cylinders = [ 405/27 ] + [783/27] + [351/27] = 15 + 29 + 13 =57
Using V = πr^2 h
27 = 22/7 *9 *h
So h = 3/ π cm
total surface area of all these cylinders = 57*(Surface area of one cylinder ) = 57*2* πr(h+r)=57*2π*3 (3/π+3)=1026(1+π)

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