Question

The radius and slant height of a cone are in the ratio 7:25.If its curved surface area is 26950cm2,find its vertical height

Answer 1

heya

your solution is given below...

according to the question, the radius and slant height of the cones are in the ratio 7 : 25

let the radius of the cone be 7x and length ( slant height ) be 25x.

CSA ( curved surface area ) of the cone = 26950cm²

therefore πrl = 26950cm²

=> 22/7 × 7x × 25x = 26950cm²

=> 175x² = 26950/1 × 7/22

=> 175x² = 1225 × 7

=> 175x² = 8575

=> x² = 8575/175

=> x² = 49

=> x = √49

=> x = 7

hence, radius of the cone = 7x

= 7 × 7

= 49cm

slant height of the cone = 25x

= 25 × 7

= 175cm

verification :-

CSA of the cone = πrl

= 22/7 × 49 × 175

= 22 × 7 × 175

= 26950cm²

hence verified..

now,

we know that Length of cone is it's slant height.

→ length ² = radius ² + height ²

→ 175 ² = 49 ² + height ²

→ 30625 = 2401 + height ²

→ 30625 - 2401 = height ²

→ 28224 = height ²

→ height = √28224

→ height = 168cm

hence, the vertical height of the cone is 168cm.

hope it will help u..