The slant height of a cone is 26 cm and base diameter is 20 cm. Find its height?
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hence the height of the cone is 24 cm
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Given,
The slant height of a cone(l) = 26cm and
The base diameter of a cone(d) = 20 cm
To find, the height of a cone(h) = ?
The radius of a cone(r) ==10cm=
2
20
=10cm
We know that,
The slant height of a cone, l=l=
r
2
+h
2
Squaring both sides, we get
⇒ l^2=r^{2}+h^{2}l
2
=r
2
+h
2
⇒ =l 2 −r
2[/tex]
⇒ h^2=26^{2}-10^{2}h
2
=26
2
−10
2
Using identity,
a^{2}-b^{2}=(a+b)(a-b)a
2
−b
2
=(a+b)(a−b)
⇒ h^2=(26+10)(26-10)h
2
=(26+10)(26−10)
⇒ h^2=36\times 16=576h
2
=36×16=576
⇒ h^2=24^2h
2
=24
2
⇒ h = 24 cm
Hence, the height of cone(h) = 24 cm
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