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  • A girl empties a cylindrical bucket full of sand, of base radius 18 cm and height 32 cm on the floor to form a conical heap of sand. If the height of this conical heap is 24 cm, then find its slant height correct to one place of de

A girl empties a cylindrical bucket full of sand, of base radius 18 cm and
height 32 cm on the floor to form a conical heap of sand. If the height of
this conical heap is 24 cm, then find its slant height correct to one place
of decimal.

 

 

 
 
 
 
 

Answers (1)

Given = Radius of the cylindrical bucket, r_{b}=18\; cm

              height of cylindrical bucket, h_b=32 \ cm

              height of conical heap,                 h_{c}=24cm

To find = slant height of the conical heap.

     in a cone,  h_{c}^{2}+r_{c}^{2}=l_{c}^{2}

We know, vol of cylindrical bucket = vol of conical heap

\Rightarrow \pi \times r^{2}_{b}h_{b}=\frac{1}{3}\pi r^{2}_{c}h_{c}

Putting values

\pi\times18^2\times32=\frac{1}{3}\pi(l_c^2-24^2)24

\Rightarrow \frac{18^{2}\times 32\times 3}{24}=l^{2}_{c}-24^{2}

\Rightarrow l^{2}_{c}=24^{2}+\frac{18^{2}\times 32\times 3}{24}

\Rightarrow l^{2}_{c}=24^{2}+4\times 18^{2}

\Rightarrow l_{}{c}=\sqrt{24^{2}+4\times 18^{2}}

\Rightarrow l_{c}=\sqrt{1872}

\Rightarrow l_{c}\simeq 43.3\; cm

Posted by

Safeer PP

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