F.3 maths question~plzz help!!

2011-08-27 11:11 am
1. A large cylindrical candle of base radius R and height R is melted and recast into 27 small cylindrical candles similar to the original one.

(a). Express the base radius of the small candle in terms of R. (ans: R/3)

(b)Find the percentage increase in the total surface area of the candles after thr process. (ans:200%)

回答 (1)

2011-08-27 4:35 pm
✔ 最佳答案
(a)
Let the radius of small cylinder be = xR
Let the height of small cylinder be = xH
x is the conversion factor 0 < x < 1, xR must be smaller than R
volume of large cylinder = 27 times volume of smaller cylinder
pi (R^2) (H) = 27 pi [(xR)^2] (xH)
(R^2) (H) = 27 (x^2)(R)^2 x(H)
(R^2) (H) = 27 (x^3)(R^2) (H)
1 = 27 (x^3)
x^3 = 1/27
x = 1/3
The base radius of the small candle = xR = (1/3) R

(b)
Surface area of large cylinder = 2(pi)R^2 + 2 (pi)RH

Total Surface area of 27 small cylinders = 27 [2(pi)(R/3)^2 + 2 (pi)(R/3)(H/3)]
= 27/9 [2(pi)(R)^2 + 2 (pi)(R)(H)]
= 3[2(pi)(R)^2 + 2 (pi)(R)(H)]
Total Surface area of 27 small cylinders = 3 times Surface area of large cylinder
Let S.A. of large cylinder be A and S.A. of 27 small cylinders be 3A

% increase = (S.A. of 27 small cylinder – S.A. of large cylinder)/ S.A. of large cylinder x 100%
= [(3A – A)/A] x 100% = [2A/A] x 100% = 200%

The percentage increase in the total surface area of the candles after the process is 200%


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