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Delaney bought a crate for her puppy when it was 3 months old. The crate is in the shape of a rectangular prism. Since the puppy is getting bigger, Delaney wants to purchase a bigger crate. She decided that the dimensions of the new crate needs to be increased by 40% of the original length. Find the missing percentage.

The volume of the new crate is exactly _________% of the old crate.

Respuesta :

Answer:

The volume of the new crate is exactly 174.4% of the old crate.

Step-by-step explanation:

Volume of a rectangular prism:

The volume of a rectangular prism of dimensions x, y and z is given by:

[tex]V = xyz[/tex]

She decided that the dimensions of the new crate needs to be increased by 40% of the original length.

Each dimension is increased by 40%, which means that each is multiplied by 1 + 0.4 = 1.4. So

[tex]V = 1.4x(1.4y)(1.4z) = (1.4)^3(xyz) = 2.744(xyz)[/tex]

Percentage:

The new volume is 2.744 the original volume. Considering the original volume is 100% = 1, it increased by 2.744 - 1 = 1.744 = 1.744*100% = 174.4%.

The volume of the new crate is exactly 174.4% of the old crate.

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