A cylindrical bucket of height 32 cm and radius 18 cm is filled with sand. The bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap.

Question

Philoid · Accepted Answer

Given, Height of cylindrical bucket(h) = 32 cm

Radius of cylindrical bucket(r) = 18 cm

Height of conical heap (H) = 24 cm

Radius of conical heap (R) = ?

⇒ Volume of cylindrical bucket = Volume of conical heap

⇒ r²h = R²H

⇒ 181832 = R²24

⇒ 181832 = R²8

⇒ R² =

⇒ R² = 18184

⇒ R =

⇒ R = 182

⇒ R = 36 cm

Slant height (L) =

L =

L = 12 cm

Slant height = 12 cm

Radius of conical heap = 36 cm