Emilburkelisagd
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A cone is placed inside a cylinder as shown. The radius of the cone is half the radius of the cylinder. The height of the cone is equal to the radius of the cylinder. What is the volume of the cone in terms of the radius, r? What is the ratio of the radius of a circle to its circumference?

Verified Answer :

taskmasters

Given:
Volume of the cone = π r² h/3

radius of the cone is half the radius of the cylinder ⇒ r/2
height of the cone is equal to the radius of the cylinder. ⇒ r

V = 3.14 (r/2)² r/3
V = 3.14 r²/4 r/3
V = 3.14r³ / 12

Lanuel

The volume of this cone in terms of the radius is V = 1/12 × πr³ and the ratio of the radius of a circle to its circumference is 1/2π.

How to calculate the volume of a cone?

Mathematically, the volume of a cone can be calculated by using this formula:

V = 1/3 × πr²h

Where:

  • h is the height.
  • r is the radius.

Based on the information given, we have:

V = 1/3 × π × (r/2)² × r

V = 1/3 × π × r²/4 × r

V = 1/12 × πr³

Also, the ratio of the radius of a circle to its circumference:

Circumference = 2πr

Where:

r is the radius of a circle.

Thus, the ratio is given by:

r/C = r/2πr = 1/2π.

Read more on circumference here: brainly.com/question/14478195

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