trig help

[Comatose]

A goat is hitched to a post by a rope of length 2 metres, so that the goat can graze a circular
patch of pasture (of radius 2 metres). The rope is lengthened to 3 metres.
The area that the goat can graze has increased by:
A. 33 1/3%
B. 50%
C. 55 5/9%
D. 125%
E. 225%

i think the answer is E
but i dunno how to show working
can someone show me how to work it out mathematically because all i did was get the 2 areas and tested each option.

[azure]

Trig?

Ermm... I wouldn't necessarily use trig for this question. Find the area of the pasture at 2 metres & 3 metres radius so...
A= pi x r^2
A|2 = 4pi
A|3 = 9pi

Then compare.

Please correct me if this method is incorrect. The answer I got was 225% as well from the method I used.

[jasoN-]

Answer should be D (125%)
The question asks for the increase in grazeable area
9pi is 225% of 4pi
but the area has only increased by (9-4)pi = 5pi
hence area increased = 5pi/4pi * 100% = 125%

[azure]

Ah right, thanks for the correction Jason. Always missing the important aspects of the question =/

[Comatose]

cheers jason and azure
i just called it trig because it was in my trig section work haha

[adRo93]

It would be in your trig section because it probably wants you to solve the area using scale factors.
2:3 = scalefactor
2^2 : 3^2 = 4:9 = ratio of areas
area of current grazing: Pi(2)^2 = 12.57
4/9 : 12.57/x (transpose to  find x)
x = 28.2825 (with larger rope)
(28.2825/12.57)x100 = 225%
225% - 100% = 125%, therefore D.

Using scalefactors to solve it seems to waste alot more time, but it is probably how your workbook wants you to solve it.