A right circular cone and a right circular cylinder have equal base and equal height. If the radius of the base and the height are in the ratio 5 : 12, then the ratio of the total surface area of the cylinder to that of the cone is (a) 3 : 1 (b) 13 : 9 (c) 17 : 9 (d) 34 : 9

Options

A. `3:1`
B. `13:9`
C. `17:9`
D. `34:9`

Answer

C

Explanation

let the radius of the base are 5k and 12k respectively
`:.("Total surface area of the cylinder")/("Total surface area of the cone ")`
`=(2pirxxh+2pir^2)/(pirsqrt(r^2+h^2+pir))`
`=(2h+2r)/(sqrt(r^2+h^2)+r)+(24k+10k)/(sqrt(25k^2+144k^2)+5k)`
`=(34k)/(13k+5k)=(34k)/(18k)=17/9or 17 :9`