Question

find the height of the right circular cone of slant height is 25 cm and area of base is 154 cm

Answer 1

Hey mate here is ur query

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Area of base =πr²=154
or r²=154/π

ir r=7

here slant height (l)=25cm
radius=(r)=7 cm
& height (h) has to find
As we know

r²+ h²= l²

or h²= l²-r²
or h=√176

or height= 13.26 cm

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Hope this will help you

Answer 2

Given,

• Area of Base = 154 cm²
• Cone of slant height = 25 cm

To Find ,

• Height of Right circular Cone = ?

Solution,

⇒We know that :

Area of base of Right circular cone = πr²

∴ $\implies \bold{154 \ cm^{2} = \pi r^{2}}$

$\implies \bold{\frac{22}{7} \times r^{2} = 154}$

$\implies \bold{ r^{2} = \frac{154 \times 7}{22}}$

$\implies \bold{ r^{2} = 49}$

$\implies \bold{ r = \sqrt{49}}$

$\implies \boxed{\bold{ r = 7 \ cm}}$

Now Find Height of Right circular cone :

⇒Suppose the height of the cone be h

We know that :

Height of Cone = $\bold{\sqrt{(Slant \ Height)^{2} - (Radius)^{2} }}$

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

$\implies \bold{ h = \sqrt{625 - 49}}$

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

$\implies \boxed{\bold{ h = 24 \ cm}}$

Therefore,

Height of Right Circular Cone = 24 cm

$\rule{200}2$

Other Formula Related to Right Circular Cone :-

• Lateral Area of right circular cone = πrl
• Total surface area of a right circular cone = π(r + l) r
• Volume of a right circular cone = 1/3π r²h