a diagonal of a cube measures 30 inches. the diagonal of a face measures $\sqrt{600}$ inches.

in inches, what is the length of an edge of the cube? round the answer to the nearest tenth.

inches

Question

a diagonal of a cube measures 30 inches. the diagonal of a face measures $\sqrt{600}$ inches.

in inches, what is the length of an edge of the cube? round the answer to the nearest tenth.

inches

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Pythagorean Theorem", "Cube Diagonals" ], "new_concepts": [], "current_concepts": [ "Pythagorean Theorem", "Cube Diagonals" ] } ## Relate the edge length to the face diagonal using the Pythagorean theorem $$ \begin{aligned} &s^2 + s^2 = d_{\text{face}}^2 \ &2s^2 = (\sqrt{600})^2 \ &2s^2 = 600 \end{aligned} $$ ## Solve for the edge length of the cube $$ \begin{aligned} &s^2 = 300 \ &s = \sqrt{300} = 10\sqrt{3} \ &s \approx 17.32 \end{aligned} $$ ## Round the edge length to the nearest tenth $$ s \approx 17.3 $$ A diagonal of a cube measures 30 inches. The diagonal of a face measures $\sqrt{600}$ inches. In inches, what is the length of an edge of the cube? Round the answer to the nearest tenth. 17.3 inches { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Pythagorean Theorem" ] }

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Question

Explanation:

Relate the edge length to the face diagonal using the Pythagorean theorem

Solve for the edge length of the cube

Round the edge length to the nearest tenth

Answer: