Question

the radii of two cylinders are in the ratio 2:3 and their heights are in the ratio 5:3. calculate the ratio of their volumes and their surface area

Answer 1

I hope it help ......

Answer 2

Let the radii of two cylinders be 2r and 3r respectively, and their heights be 5h and 3h.
let S1 and S2 be the Curved Surface ares of the two cylinders and V1 and V2 be their Volumes. Then,

S1 = Curved Surface area of the Cylinder of height 5h and 2r

= 2 pi × 2r × 5h

= 20 pi rh

S2 = C.S.A of the cylinder of height 3h and 3r

= 2 pi × 3h × 3r
= 18 pi rh
therefore,

S1/ S2 = 20 pi rh / 18 pi rh = 10/ 9 = 10: 9

V1 = volume of the cylinder of height 5h and radius 2r

= pi r^2 h
= pi 2r^2× 5
= 20 pi r^2 h


V2 = Volume of tje Cylinder of height 3h and radius 3r

= pi r^2 h
= pi × 3r^2 × 3
= 27 pi r^2 h

therefore, V1/ V2 = 20 pir^2h / 27 pi r^2h

= 20/ 27= 20:27

Hope; it helped☻☻