A cylindrical bucket, 32 cm high and 18 cm of radius of the base, is f

1.	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.
Answer» 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 = π × r² × h And, volume of cone = 1/3 π × r² × h Then, from the question Volume of the conical heap = Volume of the cylindrical bucket 1/3 π × r² × 24 = π × 18² × 32 r² = 18² x 4 r = 18 x 2 = 36 cm Now, Slant height of the conical heap (l) is given by l = √(h² + r²) l = √(24² + 36²) = √1872 l = 43.26 cm Therefore, the radius and slant height of the conical heap are 36 cm and 43.26 cm respectively.

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.

Answer»

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 = π × r² × h

And, volume of cone = 1/3 π × r² × h

Then, from the question

Volume of the conical heap = Volume of the cylindrical bucket

1/3 π × r² × 24 = π × 18² × 32

r² = 18² x 4

r = 18 x 2 = 36 cm

Now,

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

l = √(h² + r²)

l = √(24² + 36²) = √1872

l = 43.26 cm

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