Question

the figure below shows a rectangular prism. one base of the prism is shaded.
(a) write an expression to find the volume of the prism using its length, width, and height. then simplify.
volume of prism: (square\timessquare\timessquare=square) cubic units
(b) find the area of the shaded base. then, using the area of the shaded base, write an expression to find the volume of the prism and simplify.
area of shaded base: (square\timessquare=square) square units
volume of prism: (square\timessquare=square) cubic units

Explanation:

Part (a)

Step1: Write the volume formula

The volume \(V\) of a rectangular prism is given by \(V = l\times w\times h\), where \(l = 4\), \(w=6\), and \(h = 7\).
So the expression is \(4\times6\times7\).

Step2: Simplify the expression

First, \(4\times6=24\). Then \(24\times7 = 168\).

Part (b)

Step1: Find the area of the shaded base

The area \(A\) of a rectangle (the base) is \(A=l\times w\), with \(l = 4\) and \(w = 6\).
The expression is \(4\times6\), and \(4\times6=24\).

Step2: Write the volume formula using the base - area

The volume \(V\) of a prism is \(V=A\times h\), where \(A = 24\) (area of the base) and \(h = 7\).
The expression is \(24\times7\), and \(24\times7=168\).

Answer:

(a) Volume of prism: \(4\times6\times7 = 168\) cubic units.
(b) Area of shaded base: \(4\times6=24\) square units. Volume of prism: \(24\times7 = 168\) cubic units.