what is the area of the base of the cone below?

height: 8 in.
volume: $v = 52\text{ in.}^3$

choices:
- $14.7\text{ in.}^2$
- $17.3\text{ in.}^2$
- $18.5\text{ in.}^2$
- $19.5\text{ in.}^2$

Question

what is the area of the base of the cone below?

height: 8 in.
volume: $v = 52\text{ in.}^3$

choices:
- $14.7\text{ in.}^2$
- $17.3\text{ in.}^2$
- $18.5\text{ in.}^2$
- $19.5\text{ in.}^2$

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": [ "Cone Base Area" ], "current_concepts": [ "Volume of a Cone", "Cone Base Area" ] } ## State the volume formula of a cone $$ V = \frac{1}{3} \cdot B \cdot h $$ ## Substitute the given values into the formula $$ 52 = \frac{1}{3} \cdot B \cdot 8 $$ ## Solve for the base area B $$ \begin{aligned} B &= \frac{52 \cdot 3}{8} \ B &= \frac{156}{8} \ B &= 19.5 \text{ in}^2 \end{aligned} $$

(A) $14.7\text{ in}^2$

(B) $17.3\text{ in}^2$

(C) $18.5\text{ in}^2$

(D) $19.5\text{ in}^2$

{ "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 of a cone

Substitute the given values into the formula

Solve for the base area B

Answer: