Question

please solve this with detailed explanation I will mark u as-s brainliest.​

Answer 1

Answer:

20 cm

Step-by-step explanation:

Given the height of the cone, H = 30 cm

Let the small cone which is cut off at a height ‘h’ from the top.

Let the radius of the big cone be R cm, and the small cone is r cm.

The volume of the big cone V = (1/3) πR²H

The volume of smaller cone v = (1/3) πr²h

A.C.Q,

V = (1/27)v

=> 1/3πR² * 30 = 1/27 * 1/3 * πr²h

=> R²/r² * 1/h = 1/27 * 30    ---- (1)

Now, in ∆KCB and ∆KDM

∠CKB = ∠DKM (common)

∠KCB = ∠ KDM = 90°

 

∴ ∆KCB~∆KDM

∴ r/R = h/30

Place in (1), we have

(30²/h²) * 1/h = 1/27 * 30

=> (h/30)³ = (1/3)³

=> h = 10 cm

Smaller cone has been cut off at a height of (30 - 10)cm = 20 cm.

Therefore, the height = 20 cm.

Hope it helps!