# A solid cube of side 7 cm is melted to make a cone of height 5 cm , find the radius of the base of the cone .

Answers (1)

Solution:  We have ,

Volume of the cube $=(side)^3=7^3 cm^3=343cm^3$

Let the radius of the base of the cone be $r$ cm . Then ,

Volume of the cone $= \frac{1}{3}\times \frac{22}{7}\times r^2 \times 5 cm^3$

since the solid cube is melted to make a cone .

$\therefore$             Volume of the cube = Volume of the cone

$\Rightarrow$           $343=\frac{1}{3}\times \frac{22}{7}\times r^2 \times5$

$\Rightarrow$          $r^2=\frac{343\times3\times7}{22\times5}=\frac{7203}{110}=65.48\Rightarrow r=\sqrt{65.48}cm =8.09cm$

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