$\textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=51 \end{cases}\implies 51=2\pi r\implies \boxed{\cfrac{51}{2\pi }=r} \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2\qquad \implies A=\pi \left( \cfrac{51}{2\pi } \right)^2\implies A=\cfrac{51^2}{2^2\pi }\implies A\approx 206.98$

4 0

2 years ago

What is the volume of the cylinder below?

Svetlanka [38]

now, let's recall Cavalieri's Principle, "solids with equal altitudes and cross-sectional areas at each height, have the same volume".

so, even though this cylinder is slanted, it has the same cross-sectional area as a cylinder that's straight-up, whose altitude is h = 5, and radius r = 4.

$\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} h=5\\ r=4 \end{cases}\implies V=\pi (4)^2(5)\implies V=80\pi$

6 0

2 years ago