Question

A cylindrical bucket 20cm high and with radius 16 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 15 cm find the radius and slant height of the heap

Answer 1

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Answer 2

The radius and slant height of the heap are 32 cm and 35.34 cm

Step-by-step explanation:

Height of cylindrical bucket = 20 cm

Radius of bucket = 16 cm

Volume of bucket = $\pi r^2 h = \pi \times 16^2 \times 20$

A cylindrical bucket 20cm high and with radius 16 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 15 cm

So, Volume of bucket = Volume of conical heap

$\pi \times 16^2 \times 20= \frac{1}{3} \pi r^2 \times 15 \\\sqrt{\frac{16^2 \times 20}{\frac{1}{3} \times 15}}=r$

32 = r

Radius of conical heap = 32

$Slant height = \sqrt{h^2+r^2}=\sqrt{15^2+32^2}=35.34$

Hence The radius and slant height of the heap are 32 cm and 35.34 cm

#Learn more:

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.

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