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Q.

The TSA of cylinder is 231cm2 if the CSA is  23rd of the TSA. Find radius and height ____.


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Detailed Solution

To solve these types of questions it is important to note that we have first converted the data given in the question to equation and then solve them to find the answer. Also it has to be noted that there is a difference between total surface area and curved surface area: total surface area includes the area of the base and top of the cylinder as well but in curved surface we include the area of only curved surface.
Here, the total surface area of a cylinder is 2πrh+2πr2.
TSA= (2πr2+2πrh) and CSA=2πrh
now(23)(2πr2+2πrh)=2πrh(4πr2+4πrh)=6πrh
or, 4πr2=2πrh
2r=h
now
2πrh=(23​)231
2πr⋅2r=(23​)231
=r2=2.2313.4π=2.231.74 .22.3=494
Then r=72 cm
And hence h = 2r = 7 cm
Hence option 4 is correct.
 
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