Question

please help!!!
What is the approximate volume of the cylinder?



height = 52.2 cm; diameter = 20 cm

Answer 1

Volume = \(\pi r^{2}h\)

We have r = 20 cm / 2 = 10 cm -- Not much need to approximation that.
We have h = 52.2 cm -- Okay, that's a little long from 50 cm. If we use 50 cm, we'll be a little short with out estimate.
We have \(\pi = 3.14159265358979323846264338...\) Okay, if we go low again, that's not far from 3.

ShortVolume = 3*(10^2)*50 cm^3= 150*100 cm^3 = 15000 cm^3

We have r = 20 cm / 2 = 10 cm -- Not much need to approximation that.
We have h = 52.2 cm -- Okay, that's a little shy of 55 cm. If we use 55 cm, we'll be a little long with out estimate. I picked 55 cm for a reason.
We have \(\pi = 3.14159265358979323846264338...\) Okay, if we go high again, that's not far from 3.2.

LongVolume = 3.2*(10^2)*55 cm^3 = 3.2 * 5 * 11 * 100 cm^3 = 16*11*100 cm^3
LongVolume = 176*100 cm^3 = 17600 cm^3

Let's calculate the exact value and see if we land in the middle.

ExactVolume = \(\pi (10^2)\cdot 52.2\;cm^{3}\) = 16399

I like it. Feel free to express some individuality in your estimates. You don't have to do it like me or like anyone else. Just make an estimate!