Question

1. a cylindrical storage container has a radius of 4 meters and a height of 10 meters. a spherical tank has a radius of 4 meters. how many spherical tanks are needed to hold the same amount as one cylinder?

a. 1
b. 4
c. 2
d. 3

Explanation:

Step1: Calculate the volume of the cylinder

The volume formula of a cylinder is \(V_{cylinder}=\pi r^{2}h\). Given \(r = 4\) meters and \(h=10\) meters, then \(V_{cylinder}=\pi\times4^{2}\times10=\pi\times16\times 10 = 160\pi\) cubic meters.

Step2: Calculate the volume of the sphere

The volume formula of a sphere is \(V_{sphere}=\frac{4}{3}\pi r^{3}\). Given \(r = 4\) meters, then \(V_{sphere}=\frac{4}{3}\pi\times4^{3}=\frac{4}{3}\pi\times64=\frac{256}{3}\pi\) cubic meters.

Step3: Find the number of spherical tanks

Let \(n\) be the number of spherical tanks. We want \(nV_{sphere}=V_{cylinder}\), so \(n=\frac{V_{cylinder}}{V_{sphere}}=\frac{160\pi}{\frac{256}{3}\pi}\). The \(\pi\) cancels out, and \(n=\frac{160\times3}{256}=\frac{480}{256}=\frac{15}{8}\approx2\) (since we are looking for the number of whole - tanks and \(\frac{15}{8}\approx1.875\), and we need to hold the same amount, so we take the next whole number which is \(2\) when considering practical tank - holding).

Answer:

C. 2