Question

calculate the height of a cone whose slant height is 25 cm and csa is 550cm2​

Answer 1

Given:-

• CSA of cone is 550 cm².
• Slant height of cone is 25 cm.

To find:-

• Height of cone.

Solution:-

• First we will find Radius of cone by using Curved surface area of cone . Then we put Radius and slant height in slant height formula for height of cone.

We know that,

$\large \boxed{ \sf CSA \: of \: cone = \pi rl}$

In which,

• r is Radius of cone.
• l is slant height.

Slant height or l = 25 cm.

CSA of cone = 550 cm².

Put l and CSA of cone in formula,

$\implies \sf 550 = \pi r \times 25$

$\implies \sf 550 = \dfrac{22}{7} \times r \times 25$

$\implies \sf \dfrac{550 \times 7}{22} = 25r$

$\implies \sf \dfrac{3850}{22} = 25r$

$\implies \sf 175 = 25r$

$\implies \sf \dfrac{175}{25} = r$

$\implies \sf 7 = r$

Or, r = 7

Radius of cone = 7 cm.

As we know,

$\large \boxed{ \sf slant \: height = \sqrt{ {(r)}^{2} + {(h)}^{2} } }$

In which,

• r is Radius of cone.
• h is height of cone.

So,

Put slant height and r in formula,

$\implies \sf \: 25 = \sqrt{ {(7)}^{2} + {(h)}^{2} }$

$\implies \sf {(25)}^{2} = 49 +{(h)}^{2}$

$\implies \sf 625 = 49 + {(h)}^{2}$

$\implies \sf 625 - 49 = {(h)}^{2}$

$\implies \sf 576 = {(h)}^{2}$

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

$\implies \sf 24 = h$

Or, h = 24

Therefore,

Height of cone is 24 cm.