Question

the archimedes principle can be used to measure the volume of an irregularly shaped solid object, by completely submerging the object in water and measuring the volume of water displaced. suppose you completely submerge an object in a right circular cylindrical tank. the tank has a diameter of 10 centimeters and is filled with water to a depth of 10 centimeters. the object sinks to the bottom, and the water level rises by 0.9 centimeters. what is the volume of the object, rounded to the nearest cubic centimeter? 71 79 141 283 785

Explanation:

Step1: Find the radius of the cylinder

The diameter $d = 10$ cm, so the radius $r=\frac{d}{2}=\frac{10}{2}=5$ cm.

Step2: Calculate the volume of the water - displaced

The volume of a cylinder is $V=\pi r^{2}h$. Here, $r = 5$ cm and $h = 0.9$ cm. Substitute these values into the formula: $V=\pi\times(5)^{2}\times0.9=\pi\times25\times0.9 = 22.5\pi$ $cm^{3}$.

Step3: Approximate the value

Using $\pi\approx3.14$, we have $V\approx22.5\times3.14 = 70.65\approx71$ $cm^{3}$.

Answer:

71