an oval track is made by erecting semicircles on each end of a 44 m by 88 m rectangle. find the length of the track and the area enclosed by the track.

the length of the track is 314 m.
(round to the nearest whole number.)

the area enclosed by the track is
(round to the nearest whole number.)

Question

an oval track is made by erecting semicircles on each end of a 44 m by 88 m rectangle. find the length of the track and the area enclosed by the track.

the length of the track is 314 m.
(round to the nearest whole number.)

the area enclosed by the track is
(round to the nearest whole number.)

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Perimeter of Composite Figures", "Area of Composite Figures" ], "new_concepts": [], "current_concepts": [ "Perimeter of Composite Figures", "Area of Composite Figures" ] } ## Identify the dimensions of the track components Using the **Perimeter of Composite Figures** and **Area of Composite Figures** knowledge points $$ \begin{aligned} &\text{Rectangle width (diameter of semicircles), } d = 44\text{ m}\ &\text{Semicircle radius, } r = \frac{d}{2} = 22\text{ m}\ &\text{Rectangle length (straight sections), } L = 88\text{ m} \end{aligned} $$ ## Calculate the length of the track Using the **Perimeter of Composite Figures** knowledge point $$ \begin{aligned} &\text{Track Length} = 2L + 2\pi r = 2(88) + 2\pi(22)\ &\text{Track Length} = 176 + 44\pi \approx 176 + 138.23 = 314.23\text{ m}\ &\text{Rounded to nearest whole number: } 314\text{ m} \end{aligned} $$ ## Calculate the area enclosed by the track Using the **Area of Composite Figures** knowledge point $$ \begin{aligned} &\text{Enclosed Area} = \text{Area of rectangle} + \text{Area of full circle}\ &\text{Enclosed Area} = L \times d + \pi r^2\ &\text{Enclosed Area} = 88 \times 44 + \pi (22)^2\ &\text{Enclosed Area} = 3872 + 484\pi \approx 3872 + 1520.53 = 5392.53\text{ m}^2\ &\text{Rounded to nearest whole number: } 5393\text{ m}^2 \end{aligned} $$ ## Question 1 The length of the track is 314 m. ## Question 2 The area enclosed by the track is 5393 $ \text{m}^2 $. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Area of Composite Figures" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the dimensions of the track components

Calculate the length of the track

Calculate the area enclosed by the track

Answer:

Question 1

Question 2