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A cylindrical bucket, 32 cm high and with radius of base 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

User Pemistahl
by
6.7k points

1 Answer

12 votes

Answer:

36 cm

43.27 cm

Explanation:


r_1 = Radius of bucket = 18 cm


h_1 = Height of bucket = 32 cm


r_2 = Radius of cone


h_2 = Height of cone = 24 cm

The volume of the cylindrical bucket and the conical heap of sand is equal so


\pi r_1^2h_1=(1)/(3)\pi r_2^2h_2\\\Rightarrow r_2=\sqrt{(3r_1^2h_1)/(h_2)}\\\Rightarrow r_2=\sqrt{(3* 18^2* 32)/(24)}\\\Rightarrow r_2=36\ \text{cm}

The radius of the heap is 36 cm.

Slant height is given by


l=√(r_2^2+h_2^2)\\\Rightarrow l=√(36^2+24^2)\\\Rightarrow l=43.27\ \text{cm}

The slant height of the heap is 43.27 cm.

User Rorypicko
by
7.1k points
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