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KheshaAintSimpgo
Answered

The ratio of the volumes of two similar rectangular prisms is 125: 64. what is the ratio of their base areas? ​

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TrishaBwkngshtgo

[tex]\large\mathsf{MATHEMATICS}[/tex]

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PROBLEM:

The ratio of the volumes of two similar rectangular prisms is 125:64. What is the ratio of their base areas?

ANSWER:

[tex] \frac{A1}{A2} = \frac{25}{16} [/tex]

SOLUTION:

[tex] \sqrt[3]{ \frac{V1}{V2} } = \sqrt[2]{ \frac{A1}{A2} } = \frac{S1}{S1} [/tex]

[tex] \sqrt[3]{ \frac{125}{64} } = \sqrt[2]{ \frac{A1}{A2} } [/tex]

[tex] \frac{A1}{A2} = \frac{25}{16} [/tex]

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RichardDumbriguego

The formula for volume of rectangular prism is L×H×W. Based on the formula, we can actually consider the prism as a cube since we are talking about the ratio. Therefore, we have to take the cube root of each.

  • cube root of 125: 5
  • cube root of 64: 4

Then, square the ratio of corresponding sides because of formula L×W.

25:16

The ratio of the bases is 25:16.

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