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Jake has 900 cm³ of material. He uses 14. 5 cm³ to make a right triangular prism. He wants to make a second prism that is a dilation of the first prism with a scale factor of 4. How much more material does Jake need in order to make the second prism? Select from the drop-down menu to correctly complete the statement. Jake needs an additional Choose. Cm³ of material to make the second prism.

Sagot :

A ratio shows the relation between two numbers. The amount of more material that is needed by Jake is 42.5 cm³.

What is a Ratio?

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

Given that the volume of the first prism is 14.5cm³, while the scale factor is 4. Since the scale factor is applicable to dimension, and volume is always the cube of three-dimension.

Therefore, the volume of the scaled prism will be the cube the of the volume of the first prism, which can be written as,

[tex]\rm \text{Volume of the Scaled prism}= (Scale\ factor)^3 \times \text{Volume of the first prism}[/tex]

Substitute the values,

[tex]\rm \text{Volume of the Scaled prism}= 4^3 \times 14.5 = 928\ cm^3[/tex]

Since, the volume of material with Jake is 900 cm³, while the material he has already used is 14.5 cm³, thus the volume of the material that is left with Jake is 885.5 cm³(900cm³-14.5cm³).

Now, since the material needed to make the scaled prism is 928 cm³, the amount of material that is with Jake is 885.5 cm³, therefore, the amount of the material that is needed by Jake to complete the scaled prism can be written as,

The Amount of more material Needed by Jake = Amount of material needed to make the scaled prism - Amount of material left with Jake

The Amount of more material Needed by Jake = 928 cm³ - 885.5 cm³

                                                                               = 42.5 cm³

Hence, the amount of more material that is needed by Jake is 42.5 cm³.

Learn more about Ratios:

https://brainly.com/question/1504221

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