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saul85 [17]
3 years ago
5

The volume of a cone is 3πx3 cubic units and its height is x units. Which expression represents the radius of the cone’s base, i

n units? 3x 6x 3πx2 9πx2
Mathematics
2 answers:
lapo4ka [179]3 years ago
6 0

Answer:

3x

Step-by-step explanation:

Edge 2021

dalvyx [7]3 years ago
5 0

Answer:

<em>r=3x</em>

Step-by-step explanation:

<u>The Volume of a Cone</u>

The volume of a cone of radius r and height h is:

\displaystyle V=\frac{1}{3}\pi hr^2

We are given the volume of a cone is

V=3\pi x^3

Equating:

\displaystyle \frac{1}{3}\pi hr^2=3\pi x^3

Multiplying by 3:

\pi hr^2=9\pi x^3

Simplifying by pi:

hr^2=9 x^3

Since h=x:

xr^2=9 x^3

Dividing by x:

r^2=9 x^2

Taking square roots:

r=\sqrt{9 x^2}=3x

Thus: r=3x

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Three water storage containers have the same volume in the shape of a cylinder, a cone, and a sphere. The base radius of the cyl
fredd [130]

Answer:

- The ratio of the height of the cone to the height of the cylinder is 3:1

- The ratio of the height of the cone to radius of the sphere is 4:1

Step-by-step explanation:

Note that the radii of all the structures are the same.

Let the height of the cone be H and the height of the cylinder be h

The volume of each of the shapes are given below as

Volume of cylinder = πr²h

Volume of a cone = (1/3)πr²H

Volume of a sphere = (4/3)πr³

1) The ratio of the height of the cone to the height of the cylinder

To obtain this, we equate the volume of those two structures

Volume of the cone = Volume of the cylinder

(1/3)πr²H = πr²h

πr² cancels out on both sides and we're left with

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2) The ratio of the height of the cone to radius of the sphere

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(1/3)πr²H = (4/3)πr³

(1/3)πr² cancels out on both sides and we're left with

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(H/r) = (4/1)

The ratio of the height of the cone to radius of the sphere is 4:1

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4 years ago
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