Question

a brand new filled can of chicken broth is 10 cm tall and has a radius of 10 cm. mishka uses some of the broth to cook and now the broth left in the can is 6 cm high. how much broth did mishka use? round your final answer to the nearest whole number. 943 cm³ 1257 cm³ 1885 cm³ 4712 cm³

Explanation:

Step1: Calculate the volume of the original broth

The formula for the volume of a cylinder is \(V = \pi r^{2}h\).
For the original can, \(r = 10\) cm and \(h = 10\) cm.
So, \(V_{original}=\pi\times(10)^{2}\times10=\pi\times100\times10 = 1000\pi\) \(cm^{3}\).

Step2: Calculate the volume of the remaining broth

For the remaining broth, \(r = 10\) cm and \(h = 6\) cm.
So, \(V_{remaining}=\pi\times(10)^{2}\times6=\pi\times100\times6=600\pi\) \(cm^{3}\).

Step3: Calculate the volume of the used broth

\(V_{used}=V_{original}-V_{remaining}\).
Substitute the values: \(V_{used}=1000\pi - 600\pi=400\pi\).
Since \(\pi\approx3.14\), \(V_{used}=400\times3.14 = 1256\approx1257\) \(cm^{3}\).

Answer:

1257 \(cm^{3}\)