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anayajhughes0603

anayajhughes0603

02.06.2021 •

Mathematics

Please help, I’m stuck........

Please help, I’m stuck........

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Ответ:

jlang8

02.06.2021

Step-by-step explanation:

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Ответ:

joceeeeelyn2899

03.11.2021

32

Step-by-step explanation:

Given: A cone’s height and its radius are each equal to half the radius of a sphere.

Let x be the radius of the sphere, then the radius of cone =x/2

and height of the cone = x/2

The volume of sphere is given by :

$V=\dfrac{4}{3}\pi r^3$ , where r is the radius of sphere.

$\Rightarrow\ V=\dfrac{4}{3}x^3$

The volume of cone is given by :

$V=\dfrac{1}{3}\pi r^2\ h$ , where r is the radius and h is height of the cone .

$\Rightarrow\ V=\dfrac{1}{3}\pi (\dfrac{x}{2})^2(\dfrac{x}{2})\\\\\Rightarrow\ V=\dfrac{1}{24}x^3$

The number of cones would it take to equal the volume of the sphere is given by :-

$n=\dfrac{\text{Volume of sphere}}{\text{Volume of cone}}\\\\=\dfrac{\dfrac{4}{3}x^3}{\dfrac{1}{24}x^3}=32$

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