a giant pie is created in an attempt to break a world record for baking. the pie is shown below

image of a circle with center a, a central angle of 38 degrees, and diameter d = 20 ft

what is the area of the slice of pie that was cut, rounded to the nearest hundredth?

22.08 ft²
13.10 ft²
33.14 ft²
28.97 ft²

Question

a giant pie is created in an attempt to break a world record for baking. the pie is shown below

image of a circle with center a, a central angle of 38 degrees, and diameter d = 20 ft

what is the area of the slice of pie that was cut, rounded to the nearest hundredth?

22.08 ft²
13.10 ft²
33.14 ft²
28.97 ft²

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": [ "Area of a Sector" ], "current_concepts": [ "Area of a Sector", "Circle Geometry" ] } ## Calculate the radius of the pie $$ \begin{aligned} d &= 20\text{ ft} \ r &= \frac{d}{2} = 10\text{ ft} \end{aligned} $$ ## Calculate the area of the slice (sector) $$ \begin{aligned} \theta &= 38^\circ \ A_{\text{sector}} &= \frac{\theta}{360^\circ} \cdot \pi r^2 \ A_{\text{sector}} &= \frac{38}{360} \cdot \pi \cdot 10^2 \ A_{\text{sector}} &= \frac{3800\pi}{360} \approx 33.16125\text{ ft}^2 \end{aligned} $$ ## Match with the closest option $$ A_{\text{sector}} \approx 33.16\text{ ft}^2 \approx 33.14\text{ ft}^2 $$

(A) $22.08\text{ ft}^2$

(B) $13.10\text{ ft}^2$

(C) $33.14\text{ ft}^2$

(D) $28.97\text{ ft}^2$

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

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QUESTION IMAGE

Question

Explanation:

Calculate the radius of the pie

Calculate the area of the slice (sector)

Match with the closest option

Answer: