Respuesta :
Answer:
The volume of the prism in the decimal form is 26.25 inches³ and [tex]26 \frac{1}{4}\ inches^{3}[/tex]
Step-by-step explanation:
Formula
Volume of a rectangular prism = Length × Breadth × Height
As given
A rectangular prism has a length of [tex]3 \frac{1}{2}[/tex]inches, a width of 5 inches, and a height of [tex]1 \frac{1}{2}[/tex] inches.
i.e
A rectangular prism has a length of [tex]\frac{7}{2}[/tex]inches, a width of 5 inches, and a height of [tex]\frac{3}{2}[/tex] inches.
[tex]Volume\ of\ a\ rectangular\ prism = \frac{7}{2}\times 5\times \frac{3}{2}[/tex]
[tex]Volume\ of\ a\ rectangular\ prism = \frac{7\times 5\times\times 3}{2\times 2}[/tex]
[tex]Volume\ of\ a\ rectangular\ prism = \frac{105}{4}[/tex]
In mixed number
[tex]Volume\ of\ a\ rectangular\ prism =26 \frac{1}{4}\ inches^{3}[/tex]
In decimal form
[tex]Volume\ of\ a\ rectangular\ prism = 26.25\ inches^{3}[/tex]
Therefore the volume of the prism in the decimal form is 26.25 inches³ and [tex]26 \frac{1}{4}\ inches^{3}[/tex]
Answer: [tex]26\dfrac{1}{4}\text{ inches}^3[/tex]
Step-by-step explanation:
Given : In a rectangular prism , length = [tex]3\dfrac{1}{2}\text{ inches}[/tex]
[tex]=\dfrac{3(2)+1}{2}=\dfrac{7}{2}\text{ inches}[/tex]
width = 5 inches
height= [tex]1\dfrac{1}{2}\text{ inches}=\dfrac{3}{2}\text{ inches}[/tex]
Now, the volume of the prism will be :-
[tex]V= l\times w\times h\\\\=\dfrac{7}{2}\times5\times\dfrac{3}{2 }\text{ inches}^3\\\\=\dfrac{105}{4}\text{ inches}^3\\\\=26\dfrac{1}{4}\text{ inches}^3[/tex]
Hence, the volume of the prism [tex]=26\dfrac{1}{4}\text{ inches}^3[/tex]
