+2446 You are correct in stating that the new volume of the cylinder is 80% of the original right cylinder. Although this is a true observation, it does not answer what the value of the percent is.
However, what 80% tells you is that this is certainly a percent decrease.
| \(V_{\text{new}}=V_{old}-xV_{old}\) | I am subtraction a portion of the old volume to see what the decimal will be. Use substitution here. |
| \(V_{\text{new}}=0.8\pi r_{\text{old}}^2h_{\text{old}}\\ V_{\text{original}}=\pi r_{\text{old}}^2 h_{\text{old}}\) | |
| \(0.8\pi r_{\text{old}}^2 h_{\text{old}}=\pi r_{\text{old}}^2 h_{\text{old}}-x\pi r_{\text{old}}^2 h_{\text{old}}\) | Now, solve. I will factor. |
| \(0.8\pi r_{\text{old}}^2 h_{\text{old}}=\pi r_{\text{old}}^2 h_{\text{old}}(1-x)\) | I will divide both sides by \(\pi r^2 h\). This get's rid of a lot of the variables. |
| \(0.8=1-x\) | |
| \(-0.2=-x\) | |
| \(x=0.2\Rightarrow 20\%\text{ change}\) | The question asks for the percent change, so I convert from a decimal to a percent. |
