Answer:
[tex]{ \boxed{ \tt{height = \sqrt{ {(hypotenuse)}^{2} - {(adjacent)}^{2} } }}} \\ h = \sqrt{ {(12)}^{2} - {( \frac{6}{2} )}^{2} } \\ h = \sqrt{135} \: cm \\ \\ { \underline{ \blue{ \tt{⚜becker \: jnr}}}}[/tex]
The height of the cone is 11.6 centimeters.
'A cone is a shape formed by using a set of line segments or the lines which connects a common point, called the vertex, to all the points of a circular base. The distance from the vertex of the cone to the base is the height of the cone. The circular base has the measured value of radius. And the length of the cone from the vertex to any point on the circumference of the base is the slant height.'
According to the given problem.
Given,
Diameter = 6 cm
Radius = 6/2 cm
= 3 cm
Slant height (l) = [tex]\sqrt{r^{2} + h^{2} }[/tex]
⇒ l² = r² + h²
⇒ l² - r² = h²
⇒ 12² - 3² = h²
⇒ 144 - 9 = h²
⇒ h² = 135
⇒ h = √135
⇒ h = 11.6 cm
Hence, the height of the cone is 11.6 centimeters.
Learn more about cones here: https://brainly.com/question/10670510
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