Question

The Curved Surface area [csa] In a cylinder is 250cm². If the cylinder is 12cm high ,find the volume.​

Answer 1

ahemmm the so-called curved area, will be the "latereal surface area" of the cylinder, and we know that that is 250 cm², whilst the height h = 12.

`\textit{lateral area of a cylinder}\\\\ LA=2\pi rh~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ LA=250\\ h=12 \end{cases}\implies \begin{array}{llll} 250=2\pi r(12)\implies 250=24\pi r \\\\\\ \cfrac{250}{24\pi }=r\implies \cfrac{125}{12\pi }=r \end{array} \\\\[-0.35em] ~\dotfill`

`\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=(125)/(12\pi )\\ h=12 \end{cases}\implies \begin{array}{llll} V=\pi \left( \cfrac{125}{12\pi } \right)^2 (12) \\\\\\ V=\cfrac{15625}{12\pi }\implies V\approx 414.47 \end{array}`