a cone has a height of 2.5 in. and a radius of 5 in. what is the volume of the cone? (use 3.14 for $\pi$. round the answer to two decimal places.)

$32.71\text{ in.}^3$
$65.42\text{ in.}^3$
$196.25\text{ in.}^3$
$588.75\text{ in.}^3$

Question

a cone has a height of 2.5 in. and a radius of 5 in. what is the volume of the cone? (use 3.14 for $\pi$. round the answer to two decimal places.)

$32.71\text{ in.}^3$
$65.42\text{ in.}^3$
$196.25\text{ in.}^3$
$588.75\text{ in.}^3$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Volume of a Cone" ], "current_concepts": [ "Volume of a Cone", "Evaluating Expressions" ] } ## State the volume formula for a cone $$ V = \frac{1}{3}\pi r^2 h $$ ## Substitute the given values $$ \begin{aligned} r &= 5\text{ in.} \ h &= 2.5\text{ in.} \ \pi &\approx 3.14 \ V &= \frac{1}{3} \times 3.14 \times 5^2 \times 2.5 \end{aligned} $$ ## Calculate the final volume $$ \begin{aligned} V &= \frac{1}{3} \times 3.14 \times 25 \times 2.5 \ V &= \frac{1}{3} \times 3.14 \times 62.5 \ V &= \frac{1}{3} \times 196.25 \ V &\approx 65.4167\text{ in.}^3 \approx 65.42\text{ in.}^3 \end{aligned} $$

(A) $32.71\text{ in.}^3$

(B) $65.42\text{ in.}^3$

(C) $196.25\text{ in.}^3$

(D) $588.75\text{ in.}^3$

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

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Question

Explanation:

State the volume formula for a cone

Substitute the given values

Calculate the final volume

Answer: