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  • A cylindrical bucket of height 32 cm and base radius 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

A cylindrical bucket of height 32 cm and base radius 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.

Answers (1)

r = 36 cm, l = 12\sqrt{13} cm

Height of cylindrical bucket (h1) = 32 cm

Radius (r1) = 18 cm

Volume = \pi r{_{1}}^{2}h_{1}

             =\frac{22}{7}\times 18 \times 18 \times 32

Height of conical heap (h2) = 24 cm

Let radius = r2

Volume  =\frac{1}{3}\pi r_{2}^{2}h_{2}=\frac{1}{3}\times \frac{22}{7} \times r_{2}^{2}\times 24

According to question

Volume of cylindrical bucket = Volume of conical heap

\frac{22}{7}\times 18 \times 18 \times 32 = \frac{1}{3}\times \frac{22}{7}\times r_{2}^{2}\times 24

=\frac{18 \times 18 \times 32 \times 3}{24}=r_{2}^{2}

=18^{2}\times 4 = r_{2}^{2}

r_{2}=\sqrt{18 \times 18 \times 2 \times 2}

r_{2}= 18 \times 2 = 36\; cm

Slant height (l)=\sqrt{r_{2}^{2}+h_{2}^{2}}

\sqrt{36^{2}+24^{2}}

=\sqrt{1296+576}

=\sqrt{1872}

\sqrt{12 \times 12 \times 13}

l=12\sqrt{13}cm

Posted by

infoexpert23

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