the volume of a cone is $108\pi$ cubic inches. its height is 4 inches. what is the radius of the cone? round the answer to the nearest tenth if necessary.

5.2 in.
9 in.
34.7 in.
81 in.

Question

the volume of a cone is $108\pi$ cubic inches. its height is 4 inches. what is the radius of the cone? round the answer to the nearest tenth if necessary.

5.2 in.
9 in.
34.7 in.
81 in.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Volume of a Cone" ], "new_concepts": [], "current_concepts": [ "Volume of a Cone", "Radical Equations" ] } ## State the volume formula and given values $$ V = \frac{1}{3}\pi r^2 h,\quad V = 108\pi,\quad h = 4 $$ ## Substitute the values and solve for r squared $$ \begin{aligned} 108\pi &= \frac{1}{3}\pi r^2 (4) \ 108 &= \frac{4}{3}r^2 \ r^2 &= 108 \cdot \frac{3}{4} \ r^2 &= 81 \end{aligned} $$ ## Solve for the radius r $$ \begin{aligned} r &= \sqrt{81} \ r &= 9\text{ in.} \end{aligned} $$

(A) 5.2 in.

(B) 9 in.

(C) 34.7 in.

(D) 81 in.

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

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QUESTION IMAGE

Question

Explanation:

State the volume formula and given values

Substitute the values and solve for r squared

Solve for the radius r

Answer: