Hello,
The volume of a cylinder is [tex] \pi*R^{2}*h[/tex].
We have : h = 17 cm but we don't have the radius.
Therefore let's find it.
You have a rectangle triangle and one of its length is the radius of the cylinder base.
So let's apply the Pythagorean theorem.
For us : AB = 17 cm, AC = 15
AB² = AC² + BC²
17² = 15² + BC²
BC² = 17² - 15²
BC² = 289 - 225
BC² = 64
BC = √64
BC = 8 cm
Therefore the radius measures 8 cm and now we have everything to calculate the cylinder's volume.
[tex] \pi*R^{2}*h[/tex]
[tex]= \pi *8^2*17[/tex]
[tex]= 3418 cm^3[/tex]
Hope it helps !
