The height of the cone is 24 cm.
The distance along the curved surface, measured from the edge at the top to a point on the circumference of the circle at the base, is known as the slant height of an object (such as a cone or pyramid). In other words, the slant height, represented either as s or l, is the shortest distance that may be traveled along the surface of the solid.
Slant height(l)=26cm
Radius(r)=10cm
It is known that, [tex]l^{2}=r^{2}+h^{2}[/tex]
Here, h is the height of the cone.
On substituting the values,
[tex]26^{2}= 10^{2}+h^{2}[/tex]
[tex]\\676=100+h^{2}\\[/tex]
[tex]h^{2}=676-100\\[/tex]
[tex]h^{2}=576\\[/tex]
[tex]h=\sqrt{576}\\[/tex]
h=24
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