Question

e. right circular cylinder with hemispherical top
the volume is
(type an exact ans
fractions for any nu
use integers or
ression.)
90 cm
40 cm
an example get m cm

Explanation:

Step1: Calculate the volume of the cylinder

The formula for the volume of a cylinder is \(V_{cylinder}=\pi r^{2}h\). Given \(r = 40\space cm\) and \(h=90\space cm\), we have \(V_{cylinder}=\pi\times40^{2}\times90=\pi\times1600\times90 = 144000\pi\space cm^{3}\).

Step2: Calculate the volume of the hemisphere

The formula for the volume of a hemisphere is \(V_{hemisphere}=\frac{2}{3}\pi r^{3}\). Given \(r = 40\space cm\), we have \(V_{hemisphere}=\frac{2}{3}\pi\times40^{3}=\frac{2}{3}\pi\times64000=\frac{128000}{3}\pi\space cm^{3}\).

Step3: Calculate the total volume

The total volume \(V = V_{cylinder}+V_{hemisphere}\).

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Answer:

\(\frac{560000\pi}{3}\space cm^{3}\)