please help!

[jadelily1390]

How many seconds will it take to completely fill a pentagonal pyramid shaped bottle if the base is a regular pentagon, 15cm to a side, the height of the "pyramid" being 32cm(assuming these measurements are for the interior of the bottle) if the flow of liquid into the bottle starts at zero and increases at a rate of 1 milliliter per second?

 

[galactus]

Here's a start:

The volume of a pyramid is \(\displaystyle V=\frac{1}{3}\cdot \text{Area of base}\cdot \text{Height}\)

The volume of a pentagonal pyramid is \(\displaystyle V=\frac{1}{12}s^{2}\cdot h\cdot \sqrt{25+10\sqrt{5}}\)

where s=length of side of base and h=height.

The volume can also be found by using \(\displaystyle V=\frac{5}{6}ash\)

a=length of apothem, s=length of side of base, h=height.

The apothem is the distance from the center to the midpoint of a side of the pentagon

So, the apothem length is \(\displaystyle \frac{15}{2}cot(36)\approx 10.32\)

Once you find the volume, use the given fill rate to find out how long it takes to fill.

 

[jadelily1390]

so, rounded to the nearest whole second, is it 79 seconds?

 

[mmm4444bot]

Is it 79 seconds ?

My rounded answer is different.

If you would like specific help, please share what you're doing.

Cheers ~ Mark