question 21 of 40

henry constructed circle a with a radius of 4 units. he then created a sector as shown in the figure below. which of the following expressions would help him find the area of the shaded sector?

a. $\frac{315}{360}(4\pi)$

b. $\frac{45}{360}(8\pi)$

c. $\frac{315}{360}(16\pi)$

d. $\frac{45}{360}(16\pi)$

Question

question 21 of 40

henry constructed circle a with a radius of 4 units. he then created a sector as shown in the figure below. which of the following expressions would help him find the area of the shaded sector?

a. $\frac{315}{360}(4\pi)$

b. $\frac{45}{360}(8\pi)$

c. $\frac{315}{360}(16\pi)$

d. $\frac{45}{360}(16\pi)$

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 Sector", "Area of Circle" ], "new_concepts": [], "current_concepts": [ "Area of Sector", "Area of Circle" ] } ## Calculate the total area of circle A $$ \begin{aligned} r &= 4 \ \text{Area}_{\text{circle}} &= \pi r^2 = \pi (4)^2 = 16\pi \end{aligned} $$ ## Determine the central angle of the shaded sector $$ \begin{aligned} \theta_{\text{unshaded}} &= 45^\circ \ \theta_{\text{shaded}} &= 360^\circ - 45^\circ = 315^\circ \end{aligned} $$ ## Formulate the expression for the shaded sector area $$ \text{Area}_{\text{sector}} = \frac{\theta_{\text{shaded}}}{360^\circ} \cdot \text{Area}_{\text{circle}} = \frac{315}{360}(16\pi) $$

A. $\frac{315}{360}(4\pi)$

B. $\frac{45}{360}(8\pi)$

C. $\frac{315}{360}(16\pi)$

D. $\frac{45}{360}(16\pi)$

{ "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 circle A

Determine the central angle of the shaded sector

Formulate the expression for the shaded sector area

Answer: