find the area of a donut shape when the radius of the larger circle is 21 ft and the radius of the smaller circle (the hole in the donut) is 11 ft. use 3.14 for pi and round your solution to the nearest tenth.

1,008.4 \text{ ft}^2
1,763 \text{ ft}^2
1,004.8 \text{ ft}^2
1,005 \text{ ft}^2

2 fill in the blank 1 point
a circle has a diameter of 6.7 cm. what is its circumference? round your solution to the nearest tenth.

Question

find the area of a donut shape when the radius of the larger circle is 21 ft and the radius of the smaller circle (the hole in the donut) is 11 ft. use 3.14 for pi and round your solution to the nearest tenth.

1,008.4 \text{ ft}^2
1,763 \text{ ft}^2
1,004.8 \text{ ft}^2
1,005 \text{ ft}^2

2 fill in the blank 1 point
a circle has a diameter of 6.7 cm. what is its circumference? round your solution to the nearest tenth.

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Arithmetic Simplification" ], "new_concepts": [ "Area of an Annulus", "Circumference of a Circle" ], "current_concepts": [ "Arithmetic Simplification", "Area of an Annulus", "Circumference of a Circle" ] } ## Calculate the area of the donut shape $$ \begin{aligned} R &= 21\text{ ft},\quad r = 11\text{ ft},\quad \pi \approx 3.14 \ A_{\text{donut}} &= \pi R^2 - \pi r^2 \ A_{\text{donut}} &= 3.14 \times (21)^2 - 3.14 \times (11)^2 \ A_{\text{donut}} &= 3.14 \times 441 - 3.14 \times 121 \ A_{\text{donut}} &= 3.14 \times (441 - 121) \ A_{\text{donut}} &= 3.14 \times 320 = 1004.8\text{ ft}^2 \end{aligned} $$ ## Calculate the circumference of the circle $$ \begin{aligned} d &= 6.7\text{ cm},\quad \pi \approx 3.14159 \ C &= \pi d \ C &\approx 3.14159 \times 6.7 \approx 21.0486\text{ cm} \ C &\approx 21.0\text{ cm (rounded to the nearest tenth)} \end{aligned} $$ ## Question 1 1,008.4 $ft^2$

1,763 $ft^2$

1,004.8 $ft^2$

1,005 $ft^2$ ## Question 2 The circumference of the circle is 21.0 cm. { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Geometry", "Area of an Annulus" ] }

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Explanation:

Calculate the area of the donut shape

Calculate the circumference of the circle

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Question 1

Question 2