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1. In ceramics class, Robert made a cone with a radius of 2.5 inches and a height of 9 inches. What was the volume of the cone?
Use ​≈3.14 and round your answer to the nearest whole number.
2. Later, Robert made a cylinder with the same radius and height as the cone. What is the volume of the cylinder?
Use ​≈3.14 and round your answer to the nearest whole number.
3. Complete the sentence below that describes the relationship between the volumes of the cone and cylinder. Use a whole number.
The cone and cylinder have the same height and radius, so the volume of the cylinder is
____ times the volume of the cone.

Sagot :

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The volume of the cone is 58.875 cubic inches. The volume of the cylinder is 176.625 cubic inches. The volume of the cylinder is three (3) times the volume of the cone.

What is the volume of a cone and cylinder?

The volume of a cone is equal to one-third (1/3) of the area of the circular base as well as the height product.

Mathematically, the volume of a cone can be expressed as:

[tex]\mathbf{V_{cone} = \pi r ^2 \dfrac{h}{3} }[/tex]

where;

  • radius = 2.5 inches
  • height = 9 inches

[tex]\mathbf{V_{cone} = 3.14 \times (2.5 ^2)\times \dfrac{9}{3} }[/tex]

[tex]\mathbf{V_{cone} = 3.14 (2.5 ^2)\times 3 }[/tex]

[tex]\mathbf{V_{cone} =58.875\ inches ^3}[/tex]

The volume of a cylinder implies the amount of quantity of material being carried in the cylinder. The volume of the cylinder can be expressed as:

V = πr²h

V = π(2.5)² × 9

V = 3.14 × (2.5)² × 9

V = 176.625 inches³

The volume of the cylinder is three times the volume of the cone because:
[tex]\mathbf{=\dfrac{176.625 \ in^3}{ 58.875\ in^3}}[/tex]

=  3

Learn more about the volume of cone and cylinder here:

https://brainly.com/question/1310192

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