find the volume of the cone.

$v = ?\text{ cm}^3$
round to the nearest tenth

Question

find the volume of the cone.

$v = ?\text{ cm}^3$
round to the nearest tenth

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 a Cone" ], "new_concepts": [], "current_concepts": [ "Volume of a Cone" ] } ## Identify the given dimensions Using the *Volume of a Cone* knowledge point $$ \begin{aligned} r &= 2\text{ cm}\ h &= 2\sqrt{3}\text{ cm} \end{aligned} $$ ## Calculate the exact volume Using the *Volume of a Cone* knowledge point $$ \begin{aligned} V &= \frac{1}{3}\pi r^2 h\ V &= \frac{1}{3}\pi (2)^2 (2\sqrt{3})\ V &= \frac{8\sqrt{3}}{3}\pi\text{ cm}^3 \end{aligned} $$ ## Round to the nearest tenth Using the *Volume of a Cone* knowledge point $$ \begin{aligned} \sqrt{3} &\approx 1.73205\ \pi &\approx 3.14159\ V &\approx \frac{8 \times 1.73205 \times 3.14159}{3}\ V &\approx 14.51039\text{ cm}^3\ V &\approx 14.5\text{ cm}^3 \end{aligned} $$ Find the volume of the cone. $V =$ 14.5 $\text{cm}^3$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Volume of a Cone" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given dimensions

Calculate the exact volume

Round to the nearest tenth

Answer: