Question

The slant height of a cone is 26 cm and base diameter is 20 cm. Find its height?



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Answer 1

hence the height of the cone is 24 cm

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Answer 2

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) =$\dfrac{20}{2 < strong > }$=10cm=

2

20

=10cm

We know that,

The slant height of a cone, l=$\sqrt{r^{2}+h^{2}}$l=

r

2

+h

2

Squaring both sides, we get

⇒ l^2=r^{2}+h^{2}l

2

=r

2

+h

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