Question 1037863
The 7 cm sector is from part of a circumference, so   {{{7/c=210/360}}}  to get to the full circumference if it were.


{{{c/7=36/21}}}
{{{c/7=3*18/(3*7)}}}
{{{c=7(18/7)}}}
{{{c=18}}}
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What is the radius for this sector?
If x is the radius, then based on the completed circle,
{{{2pi*x=18}}}
{{{x=18/(2pi)}}}
{{{highlight(x=9/pi)}}}--------the sector's radius*.



Once the unattached sector sides are attached, the circumference of the cone becomes the 7 cm length, so {{{2pi*r=7}}};
{{{highlight(r=7/(2pi))}}}-----base radius of the cone.



*    What was the sector's radius becomes the slant height of the cone when formed.  Imagine a cross section right triangle formed in making the cone.  The cone height will be  {{{h^2+(7/(2pi))^2=(9/pi)^2}}}.
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{{{h^2=(81/pi^2)-(49/(4(pi)^2))}}}

{{{h^2=(1/pi)^2(81-49/4)}}}

{{{h^2=(1/pi)^2(324/4-49/4)}}}

{{{h^2=(1/pi)^2(275/4)}}}

{{{h=sqrt(275)/(2pi)}}}

{{{highlight(h=5*sqrt(11)/(2pi))}}}------How tall the cone



You can do the rest.