Question

A cylindrical bucket is 32cm and with radius of base 18 cm is filled with sand completely this bucket is emitted 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

Answer

• Radius = 36cm
• Slant height = 12√13 cm

Explaination

First find out the volume of the bucket filled with sand completely

Given

Height (H) = 32 cm

Radius (R) = 18 cm

Volume of the bucket = πR²H

=> π × 18 × 18 × 32

=> 10368 π cm³

Now, the sand in the bucket is emitted on the ground and a conical heap is formed.

So, the Volume of the heap will be equal to the volume of the sand in the bucket

Given

height (h) = 24 cm

=> Volume of conical heap = Volume of the bucket

=> 1/3*πR²h = 10368 π

Cancelling π from both side

=> 1/3* R² * 24 = 10368

=> R² * 8 = 10368

=> R² = 10368/8

=> R² = 1296

=> R = √(1296)

=> R = 36 cm (Radius)

we know that

Slant height = √{(base)² + (height)²}

=> Slant height = √{(36)² + (24)²}

=> Slant height = √{1296 + 576}

=> Slant height = √{1872}

=> Slant height = 12√13 cm