Question

A solid cone is melted and 3 cylindrical rods are formed from the melted metal. what is the length of a single? volume of the cone is 1968πm^2.diameter of the rod is 8 m

Answer 1

Concept

An iconic three-dimensional geometric shape called a cone has a flat surface and a curving surface that points upward. Apex and base are terms used to describe the pointy and flat portions of a cone, respectively. A cylinder is a three-dimensional solid in mathematics that maintains, at a given distance, two parallel bases connected by a curving surface. These bases often have a circular form (like a circle), and a line segment known as the axis connects the centers of the two bases.

Volume of cone is given by = $\pi r^{2} h/3$.

Volume of cylinder is = $\pi r^{2} h$

Given

A solid cone is melted and $3$ cylindrical rods are formed from the melted metal. Volume of the cone is $1968\pi m^2$.diameter of the rod is $8 m$.

To Find

We have to find the length of the cylindrical rod.

Solution

According to the problem,

Volume of cone and the three rod will be same.

∴$1968\pi =3\pi 4^{2} h$

$h=1968/48=41m$.

Hence, length of the cylinder is $41m$.

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Answer 2

Answer:

The length of each cylinder is 41m.

Explanation:

Given a solid cone is melted and 3 cylindrical rods are formed from the melted metal.

Then the volume of the cone must be equal to the volume of the three cylindrical rods.

Volume of a cone is given by

$V_{cone} =\dfrac{\pi }{3} r^{2} h$

Volume of a cylinder is given by

$V_{cylinder} =\pi r^{2} h$

Therefore,

$\dfrac{\pi }{3} r^{2} h=3\pi r^{2} h$

Given the volume of cone,  $V_{cone} =1968\pi m^2$

Thus, $3\pi r^{2} h=1968\pi$

$\implies r^{2} h=\dfrac{1968}{3}=656$

Given the diameter of the cylindrical rod, $d=8m$  

Hence, the radius of the cylinder,

$r=\dfrac{d}{2} =\dfrac{8}{2}=4m$

Using this,

$\implies r^{2} h=656\implies 4^{2} h=656$

$\implies16h=656\implies h=\dfrac{656}{16} =41m$

Therefore, the length of each cylinder is 41m.

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