Question

the cone and pyramid are each what fraction of the volume of the same dimension cylinder and prism? 1/3 1/4 1/2 rewatch submit

Explanation:

Step1: Recall volume formulas

Volume of cylinder \(V_{cylinder}=\pi r^{2}h\), volume of cone \(V_{cone}=\frac{1}{3}\pi r^{2}h\). Volume of prism \(V_{prism}=Bh\) (where \(B\) is base - area), volume of pyramid \(V_{pyramid}=\frac{1}{3}Bh\).

Step2: Find the ratio

For cone and cylinder with same \(r\) (radius) and \(h\) (height): \(\frac{V_{cone}}{V_{cylinder}}=\frac{\frac{1}{3}\pi r^{2}h}{\pi r^{2}h}=\frac{1}{3}\). For pyramid and prism with same \(B\) (base - area) and \(h\) (height): \(\frac{V_{pyramid}}{V_{prism}}=\frac{\frac{1}{3}Bh}{Bh}=\frac{1}{3}\).

Answer:

\(\frac{1}{3}\)