Math CentralQuandaries & Queries


Question from kp:

I have 2 flower pots with the following dimensions that I am trying to calculate the
volume of Soil I will need to fill them. pot #1 29"tall, top of pot 31.5 inches across( radius of 15.5") the bottom of the pot is 21"across (radius 10.5)
Pot #2 29"tall, top of pot 26 across (radius 13") the bottom of the pot 17'"a cross (radius 8.5")
thank you


In the response to a previous question Stephen and I gave a formula for finding the volume of a truncated cone, which is the shape of your pots. The expression is

\[V = \frac13 \pi \times h \times (R^2 + r \times R + r^2)\]

where $R$ is the radius of the top of the pot, $r$ is the radius of the bottom and $h$ is the height. For your first pot this gives

\[V = \frac13 \pi \times 29 \times \left( \left( \frac{31.5}{2} \right)^2 + \frac{31.5}{2} \times \frac{21}{2} + \left( \frac{21}{2} \right) ^2\right).\]

For this get 15,903.72 cubic inches.

Google will help now. Type 15903.72 cubic inches in cubic feet into the Google search engine and Google will respond with 15 903.72 (cubic inches) = 9.20354167 cubic feet. If you want the volume in liters ask Google for 15903.72 cubic inches in liters.

Now you try the second pot. Write back if you need more assistance.


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