a diagonal of a cube measures $\sqrt{150}$ cm. the diagonal of a face measures 10 cm.

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

centimeters

Question

a diagonal of a cube measures $\sqrt{150}$ cm. the diagonal of a face measures 10 cm.

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

centimeters

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" ], "new_concepts": [ "Cube Diagonals" ], "current_concepts": [ "Pythagorean Theorem", "Cube Diagonals" ] } ## Relate the face diagonal to the edge length $$ \begin{aligned} s^2 + s^2 &= 10^2 \ 2s^2 &= 100 \ s^2 &= 50 \end{aligned} $$ ## Solve for the edge length $$ \begin{aligned} s &= \sqrt{50} \ s &= 5\sqrt{2} \approx 7.071 \end{aligned} $$ ## Round to the nearest tenth $$ s \approx 7.1 $$ A diagonal of a cube measures $\sqrt{150}$ cm. The diagonal of a face measures 10 cm. What is the length, in centimeters, of an edge of the cube? Round the answer to the nearest tenth. 7.1 centimeters { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Pythagorean Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Relate the face diagonal to the edge length

Solve for the edge length

Round to the nearest tenth

Answer: