Question

The radio of two circular cylindes are
in ratio 1:20 and there height are in
the ratio 4:3 Find the ratio of
lateral surface area and volume.​

Answer 1

Answer:

The curved surface area (CSA) of a cylinder is given by: 2πrh2πrh

where r denotes the radius and h denotes the height of the cylinder.

Now, we need to find the ratio of the curved surface areas. So, we have

CSA1CSA2=2πr1h12πr2h2CSA1CSA2=2πr1h12πr2h2

where CSA1CSA1 and CSA2CSA2 denote the curved surface areas of cylinder 1 and cylinder 2 respectively, r1r1 and r2r2 denote the respective radii and h1h1and h2h2 denote the respective heights of the cylinders.

By simplifying we get:

CSA1CSA2=r1h1r2h2CSA1CSA2=r1h1r2h2

=>CSA1CSA2=r1r2∗h1h2=>CSA1CSA2=r1r2∗h1h2

Now, we are given that the ratios of the radii is 3:23:2 and ratio of the heights is 4:5.4:5.

So, by substituting r1r2=32r1r2=32 and h1h2=45h1h2=45, we get:

CSA1CSA2=32∗45CSA1CSA2=32∗45

=>CSA1CSA2=65=>CSA1CSA2=65

So, the ratio of the curved surface areas is 6:5.6:5.