question 25 of 25

a pizza with a diameter of 12 inches is cut into 8 equal slices. to the nearest square inch, what is the area of each slice of the pizza?

a. 18 \text{ in}^2
b. 14 \text{ in}^2
c. 5 \text{ in}^2
d. 28 \text{ in}^2

Question

question 25 of 25

a pizza with a diameter of 12 inches is cut into 8 equal slices. to the nearest square inch, what is the area of each slice of the pizza?

a. 18 \text{ in}^2
b. 14 \text{ in}^2
c. 5 \text{ in}^2
d. 28 \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": [ "Area of Circle" ], "new_concepts": [], "current_concepts": [ "Area of Circle", "Area of Sector" ] } ## Calculate the total area of the pizza $$ \begin{aligned} d &= 12\text{ in} \ r &= \frac{d}{2} = 6\text{ in} \ A_{\text{total}} &= \pi r^2 = \pi (6)^2 = 36\pi\text{ in}^2 \end{aligned} $$ ## Calculate the area of each slice $$ \begin{aligned} A_{\text{slice}} &= \frac{A_{\text{total}}}{8} = \frac{36\pi}{8} = 4.5\pi\text{ in}^2 \end{aligned} $$ ## Round to the nearest square inch $$ \begin{aligned} A_{\text{slice}} &\approx 4.5 \times 3.14159 \approx 14.137\text{ in}^2 \ A_{\text{slice}} &\approx 14\text{ in}^2 \end{aligned} $$

(A) $18\text{ in}^2$

(B) $14\text{ in}^2$

(C) $5\text{ in}^2$

(D) $28\text{ in}^2$

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

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QUESTION IMAGE

Question

Explanation:

Calculate the total area of the pizza

Calculate the area of each slice

Round to the nearest square inch

Answer: