Q:

A new company wants to mail out samples of its hair products. The company has a sample box that is a rectangular prism with a rectangular base with an area of 23 1/3 in². The height of the prism is 1 1/4 in. Determine the volume of the sample box.

Accepted Solution

A:
Answer:The volume of the rectangular prism is [tex]\tfrac{175}{6} in^{3}[/tex]. Step-by-step explanation:Here, box is in the shape of rectangular prism means cuboid shape. Given: Rectangular prism base area is [tex]23\tfrac{1}{3}[/tex] in². Height of the prism is [tex]1\tfrac{1}{4}[/tex] in. Calculation: Volume of the rectangular prism is nothing but the volume of cuboid. Volume of the cuboid is expressed as follow: V=lbh           …… (1) Base are of the rectangular prism is expressed as follows: A=lb             …… (2) Substitute the equation (2) in (1). We get the expression for volume as follows: V=Ah Substitute [tex]23\tfrac{1}{3}[/tex] in² for A and [tex]1\tfrac{1}{4}[/tex] in for h in above equation as follows: [tex]V=23\tfrac{1}{3}\times 1\tfrac{1}{4}[/tex][tex]V=\tfrac{70}{3}\times \tfrac{5}{4}[/tex][tex]V=\tfrac{175}{6} in^{3}[/tex]Thus, the volume of the rectangular prism is [tex]\tfrac{175}{6} in^{3}[/tex].