Question

a brand new filled jar of jam is 10 cm tall and has a radius of 5 cm. anns family eats some of the jam one weekend and now the jam in the jar is 4 cm high. approximately how much jam did anns family eat? round only your final answer to the nearest whole number. 150 cm³ 314 cm³ 471 cm³ 785 cm³

Explanation:

Step1: Calculate the initial volume of the jar

The formula for the volume of a cylinder is \(V = \pi r^{2}h\). Given \(r = 5\) cm and \(h = 10\) cm, we have \(V_{initial}=\pi\times5^{2}\times10=\pi\times25\times10 = 250\pi\) \(cm^{3}\).

Step2: Calculate the remaining volume of the jar

The height of the remaining jam is \(h_{remaining}=4\) cm. Using the volume formula \(V=\pi r^{2}h\) again, with \(r = 5\) cm and \(h = 4\) cm, we get \(V_{remaining}=\pi\times5^{2}\times4=\pi\times25\times4=100\pi\) \(cm^{3}\).

Step3: Calculate the volume of jam eaten

Subtract the remaining volume from the initial volume: \(V_{eaten}=V_{initial}-V_{remaining}\). Substitute the values: \(V_{eaten}=250\pi - 100\pi=150\pi\) \(cm^{3}\).

Step4: Approximate the value

Take \(\pi\approx3.14\). Then \(V_{eaten}\approx150\times3.14 = 471\) \(cm^{3}\).

Answer:

\(471\ cm^{3}\)