Koty's Dad or other Math Wizards?

[VaNurse]

Can you help with this? I think I've got the volume of the bottle but I'm stuck with the fill rate. I think it's "integral" but that's where I got lost.

A witch is making a special potion. For this particular potion, she's filling a bottle in the shape of a pentagonal pyramid: the base is a regular pentagon, 15cm to a side, and the height of the "pyramid" is 32cm. Assume these measurements are for the interior of the bottle.

Assume the flow of potion into the bottle starts at zero and increases at a rate of 1 millilitre per second per second. How many seconds will it take to completely fill the bottle? Please round to the nearest whole number.

TIA :0008

 

[Morris]

Let s represent the length of a side of the pentagonal base. Then the area of a 1/5 triangular sector is (s/2)(s/2)/tan 36? and thus the area of the pentagon is 5(s/2)(s/2)/tan 36? = [5/(4tan 36?)]s?. This makes the volume of the pyramid = (1/3)[5/(4tan 36?)]15? ? 32 = 4129.1458 cm?.

At the rate of 1 cm?/sec the potion's volume after t seconds is (1/2) t? cm?, so the time it takes to fill the bottle is √(2 ? 4129.1458) seconds = 90.8751 seconds.

:0023

 

[KotysDad]

I'll go along with that. I got a volume of exactly 4132 cubic centimeters, and a time of 90.9 seconds.

I used a different formula for volume though.

using t^2 + t = 8264 ...... a t=90 give 8190
so something between 90 and 91 seconds seems right.

I agree with Morris' answer. He got the more exact answer for you.

 

[LDB]

:scared

 

[kickserv]

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[Nole]

I got 4.



:0008








:00hour LOL! at kickserv!

 

[VaNurse]

Thank you for the responses! That question appeared in a weekly contest on a kids' website. It ticked me off that I couldn't figure it out.

 

[SixFive]

I agree with Nole. :0008