Question

The TSA of cylinder is $231$ ${\text{cm}}^2$ if the CSA is ${\frac{2}{3}}^{rd}$ of the TSA , find radius and height.

Answer 1

$TSA=(2\pi r^2+2\pi rh)andCSA=2\pi rhnow\left(\frac{2}{3}\right)(2\pi r^2+2\pi rh)=2\pi rh(4\pi r^2+4\pi rh)=6\pi rhor4\pi r^2=2\pi rh2r=hnow$

$=2\pi rh=\left(\frac{2}{3}\right)231$

$=2\pi r\cdot 2r=\left(\frac{2}{3}\right)231$

$=r^2=\left(\frac{2\cdot 231}{3\cdot 4\pi }\right)=\left(\frac{2\cdot 231\cdot 7}{4\cdot 22\cdot 3}\right)=\left(\frac{49}{4}\right)\therefore r=\left(\frac{7}{2}\right)cmandhenceh=2r=7cm$