Question

to the nearest cubic centimeter, what is the volume of this cylinder?
20cm³
98cm³
9021cm³
49cm³
2 multiple choice 2 points
triangle abc is a right triangle. which equation could be used to determine the length of side ac?
$x = \sqrt{7^{2}+20^{2}}$
$x = \sqrt{20^{2}-7^{2}}$
$x = 7^{2}+20^{2}$
$x = 20^{2}-7^{2}$

Explanation:

Step1: Recall the Pythagorean theorem

In a right - triangle \(ABC\) with hypotenuse \(AB = c\), and legs \(AC=x\) (let \(AC\) be \(a\)) and \(BC = b\), the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), so \(a=\sqrt{c^{2}-b^{2}}\).

Step2: Substitute the values

Here \(c = 20\), \(b = 7\), and \(a=x\). Substituting into the formula \(x=\sqrt{20^{2}-7^{2}}\).

Answer:

\(x = \sqrt{20^{2}-7^{2}}\) (the second option)