Question

The slant height and diameter of the base of a cone are 25cm, and14cm respectively then its height is ___cm

Answer 1

Answer:

24 cm

Step-by-step explanation:

h^2=l^2-r^2h=√25^2+7^2

=√576

=24 cm

Answer 2

Question:-

The slant height and diameter of the base of a cone are 25cm, and 14cm respectively then its height is ___cm

Required Answer:-

Given:-

• Slant Height of the cone = 25cm
• Diameter of the base of the cone = 14cm

To Find:-

Height of the cone.

Solution:-

We know that:-

• $\boxed{\rm{\bold{ {l}^{2} = {h}^{2} + {r}^{2} }}}$

Where,

• l = Slant Height
• h = Height
• r =- Radius of the base

We have,

• Slant height l = 25cm
• Radius of the base r = (14/2)cm = 7cm

Substituting the values:-

$\\ \bold{\tt{ {25}^{2} = {h}^{2} + {7}^{2}}}$

$\\ \tt{\implies{ {h}^{2} = {25}^{2} - {7}^{2} }}$

$\\ \tt{\implies{ {h}^{2} = 625 -49 }}$

$\\ \tt{\implies{ {h}^{2} = 576 }}$

$\\ \tt{ \implies{h = \sqrt{576}}}$

$\\ \tt{ \therefore{ \red{h = 24}}}$

Hence, the height of the cone is 24cm