The slant height of the frustum of a cone is 5cm. If the difference the radii of its two circular ends is 4 cm find the height of the frustum ?
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Secondary School Math 10 points
The slant height of the frustum of a cone is 5 cm. If the difference the radii of its two circular ends is 4 cm, write the height of the frustum.
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hp95631327 Virtuoso
The height will be 3 cm.
Explanation is in attachment....
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mysticd
mysticd Genius
Answer:
Height of the frustum (h)=3cm
Explanation:
The slant height (l) of the frustum of a cone = 5 cm
Let Radius of the larger circular face of the frustum = R cm
radius of the smaller circular
face of the frustum = r cm
According to the problem given,
R-r = 4cm.
We know that,
l=\sqrt {h^{2}+(R-r)^{2}}
\implies 5=\sqrt{ h^{2}+4^{2}}
\texttt { On \: Squaring \: both \: sides \\ of \: the \: equation \:}
5^{2}= h^{2}+4^{2}
\implies 25-16= h^{2}
\implies 9 = h^{2}
\implies \sqrt 9 = h
\implies h = 3\: cm
Therefore,
Height of the frustum (h)= 3cm
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