1. A. 2/3 of the volume of the rectangular prism crate = 5.7 ft³
B. Amount of space the dog will occupy is: 2.55 ft³. Josiah should buy the medium crate.
2. 21.05 ft²
<h3>What is the Volume of a Rectangular Prism?</h3>
The volume of a rectangular prism = (length)(width)(height).
1. Part A:
Length of the rectangular prism crate = 2.5 ft
Width = 1.7 ft
Height = 2 ft
Volume of the rectangular prism crate = (2.5)(1.7)(2)
Volume of the rectangular prism crate = 8.5 ft³
2/3 of the volume of the rectangular prism crate = 2/3(8.5) = 5.7 ft³
Part B:
Amount of space the dog will occupy = volume = (length)(width)(height).
Length = 2 ft
Height = 1 2/3 = 1.7 ft
Width = 3/4 = 0.75 ft
Amount of space the dog will occupy = volume = (2)(0.75)(1.7)
Amount of space the dog will occupy = volume = 2.55 ft³
The space the dog will occupy is less than 2/3 of the space of the crate, therefore, Josiah should buy the medium crate.
2. Amount of fabric needed to cover the crate = surface area of rectangular prism - (lw) = 2·(1.7·2.5+2·2.5+2·1.7) - (2.5)(1.7)
= 25.3 - 4.25
= 21.05 ft²
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