NeoPets Riddles (Lenny Conundrums) and Answers Here

Re: Lenny Conundrum

The circle included a bunch of grey stuff, and four tan squares of area 50 mm by 50 mm each, or 2500 sq mm each.

To find the area of the enclosed gray stuff, take the radius that was found last week, and find the area of that circle. Then subtract out the area of the four tan squares.

The difference is the gray area.

Eliz.

P.S. Is this the new Lenny?

Yes, it's the new Lenny.

new lenny
its out, but since I cannot figure out the answer from last week, since someone will think I am a lurker...

I think I have the answer.... is it 17,146 square millimeters?

last weeks answer was 7.91 cms

Can someone check and see if I got it right... I really need that lenny avatar!

~ the answer from last weeks was 7.91cm

I got 9646 square millimeters

oh wait, maybe it's only 9,646 sq. mil.

well i hope that's right cause that's what I submitted.... thanks for checking

oopsie, sorrie i didnt realize it was posted already

Okay then; follow the process listed earlier.

The circle had a radius of 7.91 centimeters, or 79.1 millimeters. The circle's area is then:

. . . . .A = (pi)(r)^2

. . . . . . .= (pi)(79.1)^2

Each of the four tan squares enclosed within the circle measures five centimeters on a side, for an area of 2500 square millimeters. With four of these, we get a total tan area of 10,000 square millimeters. Then the grey-only area inside the circle is given by:

. . . . .(pi)(79.1)^2 - 10,000

. . . . . . .= 6,256.81(pi) - 10,000

. . . . . . .= 9656.3483309... (approx)

Rounded to the nearest square millimeter, the grey-only area is 9656 square millimeters.

Please check my work.

Eliz.

yup, that's what I got.

Isn't 100 centimeters equal to 1000 millimeters.....not 10,000?

EDIT: I see what I did......I did the math then converted it at the end.....but I guess I shouldn't have

sooo the answer is 9656 square millimeters???? becouse i dont want to get it wrong

No. The answer is 9635 square mm. You can't use the rounded answer to the previous problem and expect to get an accurate answer to this problem. The square of the radius is 6250 exactly, not 6,256.81. Never round intermediate results.

Arrgh! So simple!

I took the square in the centre, plus the four half squares surrounding it, plus four segments with a chord length of 50mm, plus four segments with a chord length of sq rt ((50*50)+(50*50)), and added them all up....

but I got 9635 sq mm

strange so many different answers how do they decide what is the correct one

the diameter squared is 250 sq.cm.
the area is (d/2)^2*pi=d^2*pi/4
the area of the 4 white squares inside - 5^2 * 4 sq.cm.
250*pi/4 - 25*4 = 96.349540849362077403915211454969 sq.cm. ~ 9635 sq.mm.

(oh, and I got the checkered negg - how cool is that?)

I agree, mathematically, but I'm not sure if we're supposed to start over from the beginning on this Lenny, or if they want us to start with last week's result. The answer provided earlier starts with last week's final answer, but if one starts again from the beginning, then:

. . . . .radius of circle, as originally computed:

. . . . . . .r = (5/2)sqrt[10] = sqrt[250/4]

. . . . .radius, in millimeters:

. . . . . . .r = (10)sqrt[250/4] = sqrt[6250]

. . . . .area of one tan square, in square millimeters:

. . . . . . .A = (50)(50) = 2500

. . . . .area of circle, in square millimeters:

. . . . . . .A = (pi)(6250)

. . . . .grey area, being the circle less the four tan squares:

. . . . . . .(pi)(6250) - 4(2500) = 6250(pi) - 10,000

. . . . . . . . .= 9634.9540849... (approx)

Rounded to the nearest square millimeter, this method gives a value of 9635 square millimeters.

Which answer a person uses will depend upon the assumption made regarding the starting point for the computations.

Eliz.