Question

a cone surmounted on a hemisphere of same radii. if the surface area of a cone and hemisphere are equal find the ratio of the radius and height of the conical part

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

The ratio r:h= 1:√3

Step-by-step explanation:

Given : Radius of cone is equal to radius of hemisphere

           Surface area of cone is equal to surface area of hemisphere

To find: The ratio of the radius and height of the conical part

Let

Radius of cone = radius of hemisphere= r

Height of cone = h

Slant height of cone = l

As given

Cone is surmounted on sphere

therefore

Curved surface area of cone = Curved surface area of hemisphere

$\pi r l = 2 \pi r ^2$

$l=2r\\ \text{now as we know} \\ l=\sqrt{h^2+r^2} \\ \Rightarrow \sqrt{h^2+r^2}= 2r\\ \text { Squaring both side we get }\\ \Rightarrow h^2+r^2=(2r)^2\\ \Rightarrow h^2+r^2=4r^2\\ \Rightarrow h^2=4r^2-r^2\\\Rightarrow h^2=3r^2 \\\\\Rightarrow (\dfrac{h}{r} )^2 =3 \\\\\Rightarrow \dfrac{h}{r} =\dfrac{\sqrt{3} }{1} \\\\\Rightarrow \dfrac{r}{h} =\dfrac{1 }{\sqrt{3}}$

Hence the ratio r:h= 1:√3

#Learn more

The radius and the height of a right circular cone are in the ratio 5 : 12 and volume is 2512 cm cube find the slant height and the radius of the base of cone? Take Pi 3.14.

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