determine the volume of the shaded region. when appropriate, use the $\pi$ key on your calculator.

the volume of the shaded region is

Question

determine the volume of the shaded region. when appropriate, use the $\pi$ key on your calculator.

the volume of the shaded region is

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Volume of Prism" ], "new_concepts": [ "Composite Volume" ], "current_concepts": [ "Volume of Prism", "Composite Volume" ] } ## Identify the geometric solids Using the *Volume of Prism* knowledge point $$ \begin{aligned} &V_{\text{outer}} = w \cdot h \cdot l \ &V_{\text{inner}} = w_{\text{inner}} \cdot h_{\text{inner}} \cdot l \end{aligned} $$ ## Calculate the outer prism volume Using the *Volume of Prism* knowledge point $$ \begin{aligned} &w = 8\text{ ft},\quad h = 8\text{ ft},\quad l = 18\text{ ft} \ &V_{\text{outer}} = 8 \cdot 8 \cdot 18 = 1152\text{ ft}^3 \end{aligned} $$ ## Calculate the inner prism volume Using the *Volume of Prism* knowledge point $$ \begin{aligned} &w_{\text{inner}} = 4\text{ ft},\quad h_{\text{inner}} = 4\text{ ft},\quad l = 18\text{ ft} \ &V_{\text{inner}} = 4 \cdot 4 \cdot 18 = 288\text{ ft}^3 \end{aligned} $$ ## Subtract to find the shaded volume Subtract the inner hollow volume from the outer volume to find the remaining shaded region: $$ \begin{aligned} &V_{\text{shaded}} = V_{\text{outer}} - V_{\text{inner}} \ &V_{\text{shaded}} = 1152 - 288 = 864\text{ ft}^3 \end{aligned} $$ Determine the volume of the shaded region. When appropriate, use the $\pi$ key on your calculator. The volume of the shaded region is 864 $\text{ft}^3$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Composite Volume" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the geometric solids

Calculate the outer prism volume

Calculate the inner prism volume

Subtract to find the shaded volume

Answer: