Question

The curved surface area of a cone is double of base area,Prove that h=√3 r.

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

Given:-

The curved surface area of a cone is double of base area

To find:-

Prove that h=√3 r.

Solution:-

Let the radius of a cone=r units

Let the height of a cone=h units

Slant height of a cone = l units

The base of a cone is in the form of circle

The base area of a cone =πr^2 sq.units

Curved Surface Area of a cone =πrl sq.units

Given that

The curved surface area of a cone is double of base area

=>πrl=2×πr^2

on cancelling πr both sides

=>l=2r

we know that slant height (l)=√(h^2+r^2)

=>√(h^2+r^2)=2r

On squaring both sides then

=>(√h^2+r^2)^2=(2r)^2

=>h^2+r^2=4r^2

=>h^2=4r^2-r^2

=>h^2=3r^2

=>h=√(3r^2)

=>h=√3 r

Answer:-

height (h)=√3r for the given problem

Used formulae:-

• Curved Surface Area of a Cone =πrl sq.units.
• Slant height (l)=√(h^2+r^2)
• Base area of a cone =πr^2 sq.units

Where, l=slant height

h=height

r=radius