what is the length of a diagonal of a cube with a side length of 3 cm?

$\sqrt{18}\text{ cm}$
$\sqrt{27}\text{ cm}$
$\sqrt{33}\text{ cm}$
$\sqrt{38}\text{ cm}$

Question

what is the length of a diagonal of a cube with a side length of 3 cm?

$\sqrt{18}\text{ cm}$
$\sqrt{27}\text{ cm}$
$\sqrt{33}\text{ cm}$
$\sqrt{38}\text{ cm}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Cube Diagonals" ], "new_concepts": [], "current_concepts": [ "Cube Diagonals", "Pythagorean Theorem" ] } ## Identify the formula for the space diagonal of a cube $$ d = s\sqrt{3} = \sqrt{3s^2} $$ ## Substitute the given side length into the formula $$ \begin{aligned} s &= 3\text{ cm} \ d &= \sqrt{3 \cdot (3)^2} \ d &= \sqrt{3 \cdot 9} \ d &= \sqrt{27}\text{ cm} \end{aligned} $$

(A) $\sqrt{18}\text{ cm}$

(B) $\sqrt{27}\text{ cm}$

(C) $\sqrt{33}\text{ cm}$

(D) $\sqrt{38}\text{ cm}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Cube Diagonals" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the formula for the space diagonal of a cube

Substitute the given side length into the formula

Answer: