the height of a cone is twice the radius of its base.

what expression represents the volume of the cone, in cubic units?

$\frac{2}{3}\pi x^3$
$\frac{4}{3}\pi x^2$
$2\pi x^3$
$4\pi x^3$

Question

the height of a cone is twice the radius of its base.

what expression represents the volume of the cone, in cubic units?

$\frac{2}{3}\pi x^3$
$\frac{4}{3}\pi x^2$
$2\pi x^3$
$4\pi x^3$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Volume of a Cone" ], "new_concepts": [], "current_concepts": [ "Volume of a Cone" ] } ## Identify the given dimensions Using the *Volume of a Cone* knowledge point $$ \begin{aligned} &\text{Radius of the base, } r = x \ &\text{Height of the cone, } h = 2x \end{aligned} $$ ## Apply the volume formula Using the *Volume of a Cone* knowledge point $$ \begin{aligned} V &= \frac{1}{3}\pi r^2 h \ V &= \frac{1}{3}\pi (x)^2 (2x) \ V &= \frac{2}{3}\pi x^3 \end{aligned} $$

(A) $\frac{2}{3}\pi x^3$

(B) $\frac{4}{3}\pi x^2$

(C) $2\pi x^3$

(D) $4\pi x^3$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Volume of a Cone" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given dimensions

Apply the volume formula

Answer: