How much can the goat eat#2?

Geometry Level 3

A goat tethered with a long rope at point C can graze a circular area with a radius of 30 meters. A rectangular barn 20 m by 10 meters is built with one corner at point C. (There is no grass inside the barn.)

Find the maximum area that the goat can graze.

(Round answer to the nearest integer.)

The answer is 2513.

6 solutions

Maharnab Mitra
May 29, 2014

So, the net area is closest to 2513.

I have the same drawing in my notebook XD

Elizabeth Ramírez - 7 years ago

actually my ans. was coming 2514 as i took the area of the yellow coloured part in the above fig. 2121( 2121.428), area of red coloured part 314(314.285) and the area of the blue one 79(78.571). So, adding them up i got 2121+314+79=2514............Wrong!!!!!!

PUSHPESH KUMAR - 7 years ago

You need to add 'em up and then approximate. Because you don't know whether the decimals add up to a number more than 1 or not!

Maharnab Mitra - 7 years ago

if you would not calculate it at the first stage then you could find the right answer. It should be like 675pi+25pi+100pi= 800pi. Now multiple 800 with 3.1416 . It will give you2513.271 which means 2513

Md. Mohaiminul Islam - 6 years, 11 months ago

800 pi = 800 x 22/7 = 2514.28....800 x 3.1416 = 2513.28.....so in terms of pi,correct answer is 800 pi to be exact. ( my own solution ) ....this is mathematics both answer should be correct whether your answer is 2514 or 2513...What is important here is you have correct analysis of the problem that will lead you to the correct solution to the problem...if you are computing using a slide rule , a difference of 1 or 5 does`nt matter at all.

Mauricio Jadulos - 7 years ago

But should not the area of the shed be deducted - there is no grass there! ie answer should be 2313

Ian Melrose - 7 years ago

The area of the barn was not added in the calculation therefore there is no need to deduct it from the final answer.

Guiseppi Butel - 7 years ago

I've used the same method.

Raiyun Razeen - 7 years ago

I missed this logic of quarter circles and was working with minor sector with 90 degree angle at centre of circle.Very clear demonstration of the problem solving.Thanks.

K.K.GARG,India

Krishna Garg - 7 years ago

the correct answer is 2514.2 so it is 2514 but not 2513

siva sunil - 7 years ago

Nice representation. Congratulations.

Niranjan Khanderia - 7 years ago

Silly me I only drew a rough diagram and calculated both small areas as 10 metres in radius >_>

Cindy Wu - 7 years ago

Nice question and answer

skaid dkhu - 7 years ago

Neat diagram!

Guiseppi Butel - 7 years ago

ok. i took the ungrazed land as 20x20

Bala Haren - 7 years ago

its answer should be (800*22)/7=2514.285=2514; if any one can take pi=3.1416..... then answer should be wrong...

Suman Singh - 7 years ago

My answer came 2512 and it was wrong! Noooooooooooo!!!

Deeksha Das - 6 years, 11 months ago

Exactly the same than me

Isaac Arce Aguilar - 6 years, 6 months ago

Elizabeth Ramírez
May 28, 2014

The area is composed by 3/4 of a big 30 m radius circle which area is 675π, the next is 1/4 of a 20m radius circle which area is 100π and 1/4 of a 10m radius circle which area is 25π, at the end we have 675π+100π+25π=2513.27

2512 should be accepted as the correct answer. The logic is perfectly alright and it's only a matter of what value of PI is being taken. Alternatively to avoid ambiguity the value of PI should be specified before hand.

saurabh dwivedy - 7 years ago

Pi is pi. Pi is not 3.14, 22/7, or anything else. Pi is pi.

Frodo Baggins - 7 years ago

In that case the correct answer should have had 800*PI as the answer. Because PI is PI and you are very very right in saying so. Then approximations etc. have no meaning.

saurabh dwivedy - 7 years ago

It did say, to nearest integer. 2513 is unambiguously correct, imho.

Barry Evans - 7 years ago

i agree that pi value must be specified to avoid confusions

Mauricio Jadulos - 7 years ago

Glad to have 3 chances to answer. I use phi as 22/7 get 2514 but wrong. I use phi as 3.14 get 2512 but also wrong. Well, I try 2513 and its correct

Suradnyana Wisnawa - 7 years ago

TOTAL AREA ACCESSIBLE= 3/4 of C.Area, r=30 m + 1/4 of C.Area, r=20 m + 1/4 of C.Area, r=10 m

TOTAL AREA ACCESSIBLE=[ 3/4(22X30x30/7) + 1/4(22X20X20 /7) + 1/4(22X10X10/7)] SQ.MTR

TOTAL AREA ACCESSIBLE=( 2121.43 + 314.30 + 78.57 ) SQ.MTR

TOTAL AREA ACCESSIBLE= 2514.30 SQ.METER

Zakaria Ameen - 7 years ago

I took pi value as3.14 .Thats why i get 2512

Brahmam Meka - 7 years ago

You have to use at least one more significant figure in all calculations than you will put in the answer. The answer is a four-digit integer, so you need to use at least 5 sig. fig.s of pi. Never round in intermediate steps.

Sophie Crane - 7 years ago

i thought in that way .. a=(22/7 * 30square) - (20 * 10 ) = 2627

Sherif Abozahw - 7 years ago

Arko Bhaumik
May 26, 2014

From the given figure, it is evident that the animal can graze 75% of the total circular zone with 30 m as radius before being obstructed by the barn. Calculating this area, it gives approximately 2120.575 sq m. Then at the lower left vertex of the barn, the rope can get folded and hence reduced to a length of 20 m (30-10). Here we have an additional zone over which the animal can graze, and its area is equal to one quadrant of a circle with radius 20 m, which gives 314.159 sq m. Then finally, at the upper right vertex, the rope folds again and has its length reduced to 10 m (30-20). Here again there is one quadrant of a circle with radius 10 m, which is 78.5398 sq m. Adding the three up, and answering to the nearest correct integral value, one has 2513 sq m.

Allan Salazar
May 29, 2014

π(30)^2 (3/4) + π(20)^2 *(1/4) +π(10)^2 (1/4) = 800π (~2513 sq.m)

Bhanu Prasad
May 29, 2014

The total area is 3/4 th of area of circle of radius 30m + 1/4 th area of circle of radius 20m + 1/4 th the area of circle of radius 10m = 3/4(900pi)+1/4(500pi)=2513.272~2513 .

Haries Ajrun
Jun 3, 2014

Well I tried 2512, 2514 and finally 2513. All of these answers are possible, please reconsider the number before making the question

How much can the goat eat#2?

The answer is 2513.

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