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# A solid cube of side $7{\text{ cm}}$ is melted to make a cone of height $5{\text{ cm,}}$ find the radius of the base of the cone.$A.\,{\text{8}}{\text{.09cm}} \\ {\text{B}}{\text{. 4}}{\text{.89cm}} \\ {\text{C}}{\text{. 6}}{\text{.14cm}} \\ {\text{D}}{\text{. 7}}{\text{.54cm}} \\$

Last updated date: 13th Sep 2024
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Hint: Cube is the three-dimensional solid object surrounded by the six square faces or the sides with the three meeting at each vertex and has six faces, twelve edges and eight vertices. Cone is the three dimensional object with the circular base joining with the help of slant height. Here the cube is melted and moulded in the form of the cone, so the volume of cone will be equal to the volume of the cube. Also, find the relation among the known and unknown terms. Use general formula for the volume of the cone, $V = \dfrac{1}{3}\pi {r^2}h$ and the volume of the cube, $V = {l^3}$

Complete step by step solution: Length of the side of the cube is $l = 7cm$
As we know that volume,
$V = {l^3} \\ V = {7^3} \\ V = 343c{m^3}\;{\text{ }}.....{\text{ (1)}} \\$
Now, volume of the cone,
$V = \dfrac{1}{3}\pi {r^2}h$
Substitute, $V = 343c{m^3}$ as the volume of cube is equal to the volume of cone, also substitute the value of height
$343 = \dfrac{1}{3} \times \dfrac{{22}}{7} \times {r^2} \times 5$
Make “r” the subject and take all the terms on left hand side
${r^2} = \dfrac{{343 \times 3 \times 7}}{{22 \times 5}} \\ {r^2} = 65.48 \\$
Take square roots on both the sides of the equation.
$r = 8.09cm$
The required solution is - The radius of the base of the cone is $r = 8.09cm$
Hence, from the given multiple choices, the option A is the correct answer.

Note: Always check the unit of measurements i.e. in metres, centimetres and litres. Always check the parameters of the given radius and diameter given and other terms. Convert units of the given terms wherever applicable.