Question

(a) write an expression to find the volume of the prism using its length, width, and height. then simplify.
volume of prism: $\square \times \square \times \square = \square$ 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: $\square \times \square = \square$ square units
volume of prism: $\square \times \square = \square$ cubic units

Explanation:

Part (a)

Step1: Recall volume formula for rectangular prism

The volume \( V \) of a rectangular prism is given by the formula \( V = \text{length} \times \text{width} \times \text{height} \). From the diagram, the length is \( 7 \), the width is \( 5 \), and the height is \( 9 \). So we substitute these values into the formula: \( 7 \times 5 \times 9 \).

Step2: Simplify the multiplication

First, multiply \( 7 \times 5 = 35 \). Then, multiply \( 35 \times 9 = 315 \).

Step1: Find the area of the shaded base

The shaded base is a rectangle with length \( 7 \) and width \( 5 \). The area \( A \) of a rectangle is \( A = \text{length} \times \text{width} \), so \( 7 \times 5 = 35 \) square units.

Step2: Find the volume using the base area

The volume of a prism is also given by \( V = \text{base area} \times \text{height} \). We know the base area is \( 35 \) and the height is \( 9 \), so we substitute these values: \( 35 \times 9 \).

Step3: Simplify the multiplication

\( 35 \times 9 = 315 \) cubic units.

Answer:

\( 7 \times 5 \times 9 = 315 \) cubic units

Part (b)