Question

A cylindrical bucket of height 32 cm and base radius 18 cm is filled with sand. This 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.

Answer 1

Given, radius of the base of the bucket = 18 cm

Height of the bucket = 32 cm

So, volume of the sand in cylindrical bucket

= πr²h

= π(18)² × 32

= 10368π

Also, given height of the conical heap (h) = 24 cm

Let radius of heap be r cm.

Then, volume of the sand in the heap

= `1/3 pir^2h`

= `1/3 pir^2 xx 24`

= 8πr²

According to the question,

Volume of the sand in cylindrical bucket = Volume of the sand in conical heap

⇒ 10368π = 8πr²

⇒ 10368 = 8r²

⇒ r² = `10368/8` = 1296

⇒ r = 36 cm

Again, let the slant height of the conical heap = l

Now, l² = h² + r²

= (24)² + (36)²

= 576 + 1296

= 1872

∴ l = 43.267 cm

Hence, radius of conical heap of sand = 36 cm

And slant height of conical heap = 43.267 cm