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A farmer must decide whether to build a cylindrical grain silo with a radius r, or a rectangular grain silo with a width rand length 2r. Both silos have the same heighth
Which has the greater ratio of volume to visible surface area? Explain.

Sagot :

jbaca1217

Answer:

The cylinder has the greater ratio because the ratio for the cylinder is rh/r+2h and the ratio for the rectangular prism is rh/r+3h

Step-by-step explanation:

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The ratio of the cylindrical grain silo and rectangular grain silo is π/2.

What is a Ratio?

A ratio shows us the number of times a number contains another number.

As it is given that the radius of the cylindrical grain silo is r, while the height is h. Therefore, the volume of the cylindrical grain silo is,

[tex]\text{Volume of Cylindrical grain silo} = \pi r^2 h[/tex]

Also, it is mentioned that the width of the rectangular grain silo is r, while the length of the rectangular grain silo is 2r. And the height of the rectangular grain silo is h. Therefore, the volume of the rectangular grain silo is,

[tex]\text{Volume of rectangular grain silo} = r \times 2r \times h = 2r^2 h[/tex]

Now, the ratio of the cylindrical grain silo and rectangular grain silo can be written as,

[tex]\dfrac{\text{Volume of Circular grain silo}}{\text{Volume of rectangular grain silo}}=\dfrac{\pi r^2 h}{2 r^2 h}\\\\\\\dfrac{\text{Volume of Circular grain silo}}{\text{Volume of rectangular grain silo}}=\dfrac{\pi}{2}[/tex]

Hence,  the ratio of the cylindrical grain silo and rectangular grain silo is π/2.

Learn more about Ratio:

https://brainly.com/question/1504221

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