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1)If the diameter of the cross-section of a wire is decreased by 5%,by what percentage should the length be increased so that the volume remains the same? |
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Answer» V = pi.h.r^2 (cylinder) When diameter is decreased by 5%, radius also is decreased by 5%. So new radius is 19r/20. So V becomes pi.h.(19r/20)^2 = pi.h.(361r^2)/400. But you want to maintain the volume at a constant, so h is to be multiplied by 400/361 to keep it constant. So length is to be incresed by 400/361 - 1 = 39/361 times, i.e. 39 x 100/361 = 10.8033 % Diametre be dradius be d/2vol=πr*r*h =πd*d*h/4if d is increased by 5% then d- 5%of dd-5/100*dd-d/2019d/20∴r=2*19d/20=19d/40vol=πd*d*h/4π*19d/40*19d/40*h∴h=400d/361 ( calculate the above one)increase in length=400h/361-l=39l/361%of increase =39h/361/h*100=3900/361% =10.80% |
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