determine the shaded area.

the shaded area is
(type an integer or decimal rounded to the nearest hundredth as needed.)

Question

determine the shaded area.

the shaded area is
(type an integer or decimal rounded to the nearest hundredth as needed.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Area of Circle", "Shaded Area" ], "new_concepts": [], "current_concepts": [ "Area of Circle", "Shaded Area", "Semicircle Area" ] } ## Calculate the area of the outer semicircle $$ \begin{aligned} &d_{\text{outer}} = 10\text{ in.} \ &r_{\text{outer}} = \frac{10}{2} = 5\text{ in.} \ &A_{\text{outer}} = \frac{1}{2} \pi r_{\text{outer}}^2 = \frac{1}{2} \pi (5)^2 = 12.5\pi\text{ sq. in.} \end{aligned} $$ ## Calculate the area of the inner semicircle $$ \begin{aligned} &d_{\text{inner}} = 5\text{ in.} \ &r_{\text{inner}} = \frac{5}{2} = 2.5\text{ in.} \ &A_{\text{inner}} = \frac{1}{2} \pi r_{\text{inner}}^2 = \frac{1}{2} \pi (2.5)^2 = 3.125\pi\text{ sq. in.} \end{aligned} $$ ## Calculate the shaded area $$ \begin{aligned} &A_{\text{shaded}} = A_{\text{outer}} - A_{\text{inner}} \ &A_{\text{shaded}} = 12.5\pi - 3.125\pi = 9.375\pi \ &A_{\text{shaded}} \approx 9.375 \times 3.14159265 \approx 29.4524\text{ sq. in.} \ &A_{\text{shaded}} \approx 29.45\text{ sq. in.} \end{aligned} $$ The shaded area is 29.45 $\text{sq. in.}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Semicircle Area" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Calculate the area of the outer semicircle

Calculate the area of the inner semicircle

Calculate the shaded area

Answer: