Question

If ratio of volume two cones are 4:5 and ratio of its radius are 4:5. Find ratio of its height

Answer 1

let the heights of two cones H , h
radii are R, r
volumes are V, v

ratio of volumes of two cones = 4:5

[1/3*π*R²*H]/[1/3*π*r²*h] =4/5

after cancellation
R²*H/r²*h = 4/5

(R/r)² *(H/h) =4/5

(4/5)²*(H/h) =4/5

H/h = 4/5 * (5²/4²)

therefore H/h= 5/4

H:h = 5:4

Answer 2

let height of 1st and 2nd cone be H and h
and radius be R and r
so .. R/r =4/5

(Vol.)1 / (Vol) 2 = 4/5

1/3 ×pi × R^2×H / 1/3 ×pi×r^2×h =4/5

(R/r)^2 ×(H/h) =4/5

( 4/5)^2× (H/h) =4/5

16/25 ×( H/h) =4/5

( H/h) = 4/5 × 25 /16
= 5/4

so..ratio of their heights

(H/h) = 5/4 ...ans......