Question

The slant height of cone is 26cm and base of diameter is 20cm .find it height

Answer 1

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}=10cm

We know that,

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

Squaring both sides, we get

⇒ l^2=r^{2}+h^{2}

⇒ h^2=l^{2}-r^{2}

⇒ h^2=26^{2}-10^{2}

Using identity,

a^{2}-b^{2}=(a+b)(a-b)

⇒ h^2=(26+10)(26-10)

⇒ h^2=36\times 16=576

⇒ h^2=24^2

⇒ h = 24 cm

Hence, the height of cone(h) = 24 cm