Question

a cylindrical bucket 32cm height and 18 centimetre of radius of base is filled with sandThe bucket is empty of the ground and the conical heap of the sand is formed if the height of the conical heap is 24 cm then find the radius of heap​

Answer 1

QUESTION :-

a cylindrical bucket 32cm height and 18 centimetre of radius of base is filled with sandThe bucket is empty of the ground and the conical heap of the sand is formed if the height of the conical heap is 24 cm then find the radius of heap & slant height .

SOLUTION :-

➠ A sand in cylinderical bucket is emptied to make a conical heap,

➠ volume of cylinder bucket = volume of conical heap.

➠ Now, first calculate volume of cylinder bucket.

➠ r = 18 cm, h = 32cm.

➠ volume of cylinder bucket = πr²h

➠volume of cylinder bucket = π × (18)² × 32

➠ volume of cylinder bucket = π × 18 × 18 ×32

➠ Now, calculate volume of conical heap.

➠ h = 24cm, r = ? , h =?

➠ volume of conical heap = ⅓πr²h

➠ volume of conical heap = ⅓ × π × (r) ² × 24

➠volume of conical heap = 8πr²

➠ volume of cylinder bucket = volume of conical heap.

➠ π × 18 × 18 ×32 = 8πr²

➠ r ² = 18×18×4

➠ r² = 1296

➠ .°. r =36cm.

➠ Now, calculate slant height .

➠ we know that, l²= h²+r²

➠ l² = (24)² + (36)²

➠ l² = 576 + 1296

➠ l² = 1872

➠ .°. l = √1872

➠.°. l =12√13cm.

ANSWER :- radius is 36cm & slant height is 12√13cm.