• 0
Newbie

# A cylindrical bucket, 32 cm high and 18 cm of radius of the base, 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.

• 0

Very important question of mensuration including
very important concept of it.need solution!
Rd sharma class 10 maths exercise-16.1 mensuration.

we have to find the radius and slant height of the heap
a cylindrical bucket, 32 cm high and
18 cm of radius of the base, 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.

Share

1. Given,

Height of the cylindrical bucket = 32 cm

Radius of the cylindrical bucket = 18 cm

Height of conical heap = 24 cm

We know that,

Volume of cylinder = Ï€ Ã— r2 Ã— h

And, volume of cone = 1/3 Ï€ Ã— r2 Ã— h

Then, from the question

Volume of the conical heap = Volume of the cylindrical bucket

1/3 Ï€ Ã— r2 Ã— 24 = Ï€ Ã— 182 Ã— 32

r2 = 182 x 4

r = 18 x 2 = 36 cm

Now,

Slant height of the conical heap (l) is given by

l = âˆš(h2 + r2)

l = âˆš(242 + 362) = âˆš1872

l = 43.26 cm

Therefore, the radius and slant height of the conical heap are 36 cm and 43.26 cm respectively.

• 0