Question

valeria purchases a can of chicken noodle soup and a can of tomato soup. the can of chicken noodle soup has a height of 4 inches and a radius of 2 inches. what is the volume of the can of chicken noodle soup?
round your answer to the nearest whole number.
cubic inches
the can of tomato soup has the same volume, but a radius of 2.5 inches. what is the height of the can of tomato soup?
round your answer to the nearest tenth.
inches

Explanation:

Step1: Calculate the volume of the chicken noodle soup can

The formula for the volume of a cylinder is \(V = \pi r^{2}h\). For the chicken - noodle soup can, \(r = 2\) inches and \(h = 4\) inches.

$$V=\pi\times(2)^{2}\times4=\pi\times4\times4 = 16\pi\approx16\times3.14 = 50.24\approx50$$

Step2: Calculate the height of the tomato soup can

Since the volume of the tomato soup can \(V = 50.24\) (same as the chicken - noodle soup can) and \(r = 2.5\) inches. Using the formula \(V=\pi r^{2}h\), we can solve for \(h\).

$$h=\frac{V}{\pi r^{2}}$$

Substitute \(V = 50.24\) and \(r = 2.5\)

$$h=\frac{50.24}{\pi\times(2.5)^{2}}=\frac{50.24}{3.14\times6.25}=\frac{50.24}{19.625}\approx2.6$$

Answer:

50 cubic inches
2.6 inches