Question

in the formula \\( \pi r^{2}h \\), \\( r \\) represents what?

a. volume
b. diameter
c. height
d. radius

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. 2
b. 3
c. 1
d. 4

Explanation:

Step1: Recall volume formulas

Volume of cylinder \(V_{cylinder}=\pi r^{2}h\), volume of sphere \(V_{sphere}=\frac{4}{3}\pi r^{3}\).

Step2: Substitute given values

Given \(r = 4\) m, \(h=10\) m. \(V_{cylinder}=\pi\times4^{2}\times10 = 160\pi\) \(m^{3}\). \(V_{sphere}=\frac{4}{3}\pi\times4^{3}=\frac{256}{3}\pi\) \(m^{3}\).

Step3: Find number of spheres

Let \(n\) be the number of spheres. \(n\times V_{sphere}=V_{cylinder}\). \(n=\frac{V_{cylinder}}{V_{sphere}}=\frac{160\pi}{\frac{256}{3}\pi}=\frac{160\times3}{256}=\frac{480}{256}=\frac{15}{8}\approx2\) (since we are looking for whole - number of tanks and we need to hold at least the same amount).

Answer:

a. 2