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PLEASE HELP! Manufacturers often alter different packages to save money and to grab customers attention. Explain using an example, how changes in the dimensions of common geometric shapes will affect the volume of the following shapes: prisms, cylinders, cones and spheres.

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Answer:

Increase or decrease the dimensions of objects. See below for an explanation!

Explanation:

An amazon box, which is a rectangular prism, is an example of a prism. If you increase the height, length, or width of the box, you can fit more stuff inside.

A cup is an example of a cylinder; by increasing the height or radius of the cup, you can fit more of a drink inside.

An icecream cone is an example of a cone; if the height or radius were increased, you might fit more ice cream inside.

A soccer ball is an example of a sphere; increasing the radius makes it larger, and various sizes are available for different levels.

You may also shrink the dimensions for each of these objects to make them smaller.

Hope this helps!

User Bluecricket
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Answer:

An example of a prism could be a an amazon box to represent a rectangular prism. As the height, length, or width of the box increases, the volume increases allowing more items to fit within the box.

An example of a cone would be an ice cream cone. As the height or the radius of the cone increases, the more volume the cone can hold, meaning more ice cream for you.

An example of a cylinder could be a cup. As the height or the radius of the cup increases, the larger the volume. More drink for you.

An example of a sphere would be a soccer ball. As the radius increases, the volume of the ball increases. Hence, larger soccer balls have a bigger radius than smaller soccer balls. This allows for different varients of the ball to be created (i.e., youth, highschool, college, pro).

Note, the volume can also be decreased by simply shrinking the measurements instead of increasing them.

Explanation:

Let's simply look at the equations of each shape.

Volume of a prism = base * height

Volume of a cone = Pi * r^2 * (height/3)

Volume of a cylinder = Pi * r^2 * height

Volume of a sphere = (4/3) Pi r^3

Notice that the volumes of prisms, cones, and cylinders directly correlate to height. As height increases, the volume increases. The sphere is unique in that the height is 2 * radius; however, the volume is related to the cube of the radius. Consider if you expanded the radius of the sphere, the volume will increase.

User Lah
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