Question

john lost his hose and is filling his rectangular swimming pool with water using a cylindrical garbage can. the pool has a length of 15 m. a width of 5 m. and a depth of 2 m. if the garbage can has a height of 1 m and a diameter of 80 cm., how many times will he have to fill his garbage can in order to fill his pool?

Explanation:

Step1: Calculate the volume of the pool

The volume \(V_{pool}\) of a rectangular prism (pool) is given by \(V = l\times w\times h\). Here, \(l = 15m\), \(w = 5m\), \(h = 2m\).

$$V_{pool}=15\times5\times2=150m^{3}$$

Step2: Calculate the radius of the can

The diameter \(d = 80cm=0.8m\), so the radius \(r=\frac{d}{2}=\frac{0.8}{2}=0.4m\)

Step3: Calculate the volume of the can

The volume \(V_{can}\) of a cylinder is given by \(V=\pi r^{2}h\). Here, \(r = 0.4m\), \(h = 1m\)

$$V_{can}=\pi\times(0.4)^{2}\times1=\pi\times0.16\approx0.5024m^{3}$$

Step4: Calculate the number of times the can is filled

Let \(n\) be the number of times. Then \(n=\frac{V_{pool}}{V_{can}}\)

$$n=\frac{150}{0.5024}\approx298.57$$

Answer:

\(299\)