Question

a circular swimming pool has a diameter of 8.6 m. it is filled with water to a height of 1.6 m. how much water is in the pool, to the nearest hundred litres? hint: 1000 l = 1 m³. a) 98 500 l b) 93 800 l c) 99 900 l d) 92 900 l

Explanation:

Step1: Find the radius of the pool

The diameter $d = 8.6$ m, so the radius $r=\frac{d}{2}=\frac{8.6}{2}=4.3$ m.

Step2: Calculate the volume of the water - filled part of the pool

The pool is a cylinder, and the volume formula for a cylinder is $V=\pi r^{2}h$. Here, $h = 1.6$ m. So $V=\pi\times(4.3)^{2}\times1.6=\pi\times18.49\times1.6\approx3.14\times18.49\times1.6 = 3.14\times29.584=92.99376$ $m^{3}$.

Step3: Convert the volume from cubic - meters to liters

Since $1$ $m^{3}=1000$ L, then $V = 92.99376\times1000 = 92993.76$ L. Rounding to the nearest hundred liters, $V\approx92900$ L.

Answer:

a) 92900 L