Archive
21st of September 2015
Mathematics
Q:

a cube and cuboid have same volume, the dimensions of cuboid are in the ratio 1:2:4, if the difference between cost of polishing the cube and cuboid @ Rs 5 per sq. m is Rs 80, find the volumes?

Nisha_vini29 - CBSE - Class IX

Monday, September 21, 2015 at 14:43:PM

A:

L e t space t h e space s i d e s space o f space t h e space c u b o i d space b e space x comma space 2 x space a n d space 4 x. L e t space t h e space s i d e space l e n g t h space o f space t h e space c u b e space b e space apostrophe a apostrophe. V o l u m e s space o f space b o t h space a r e space e q u a l. space H e n c e comma space 8 x cubed equals a cubed rightwards double arrow open parentheses a over x close parentheses cubed equals 8 rightwards double arrow a over x equals 2 S u r f a c e space a r e a space o f space t h e space c u b e space i s space 6 a squared space a n d space t h a t space o f space t h e space c u b o i d space i s space 2 open parentheses 14 x squared close parentheses equals 28 x squared G i v e n space t h a t space open vertical bar open parentheses 6 a squared minus 28 x squared close parentheses 5 close vertical bar equals 80 rightwards double arrow open vertical bar 6 a squared minus 28 x squared close vertical bar equals 16 rightwards double arrow open vertical bar 6 open parentheses a over x close parentheses squared minus 28 close vertical bar equals 16 over x squared rightwards double arrow open vertical bar 24 minus 28 close vertical bar equals 16 over x squared rightwards double arrow x squared equals 4 rightwards double arrow x equals 2 V o l u m e space o f space t h e space c u b o i d equals 8 x cubed equals 8 cross times 8 equals 64 equals V o l u m e space o f space t h e space c u b e.

Monday, September 21, 2015 at 18:12:PM