Question

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.

Answer 1

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:

$V = xyz$

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

$V = 1.4x(1.4y)(1.4z) = (1.4)^3(xyz) = 2.744(xyz)$

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.