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A metallic solid cone is melted and cast into a cylinder of the same base as that of the cone. If the height of the cylinder is $7 cm$ . What was the height of the cone?

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20 cm

21 cm

22 cm

12 cm

answer is B.

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Detailed Solution

Given that,
Height of the cylinder is

7 cm

.
When a solid of one shape is melted into another shape, the amount of volume remains the same.
Volume of cone

=

\frac{1}{3} π r_{}^{2} h_{}

Volume of cylinder

= π r_{}^{2} h_{}

Let

r_{1} and r_{2}

be radius of cone and cylinder respectively also

h_{1}

and

h_{2}

be height of cone and cylinder respectively.
Volume of cone

=

Volume of cylinder

\Rightarrow \frac{1}{3} π r_{1}^{2} h_{1} = π r_{2}^{2} h_{2}

\Rightarrow \frac{1}{3} \times r^{2} \times h_{1} = r^{2} \times 7 [r_{1} = r_{2} = r as same base]

\Rightarrow h_{1} = 7 \times 3 = 21 cm

Therefore, height of cone is

21

cm.
Hence, the correct option is 2.

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