8 what is the area of an annulus with circles of radii $17\text{ cm}$ and $8.5\text{ cm}$? answer in square centimetres correct to one decimal place.

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Annulus Area" ], "new_concepts": [], "current_concepts": [ "Annulus Area", "Circle Area" ] } ## Identify the given radii and formula $$ \begin{aligned} &R = 17\text{ cm}\ &r = 8.5\text{ cm}\ &A = \pi(R^2 - r^2) \end{aligned} $$ ## Calculate the area of the annulus $$ \begin{aligned} &A = \pi(17^2 - 8.5^2)\ &A = \pi(289 - 72.25)\ &A = 216.75\pi\ &A \approx 680.9402\text{ cm}^2 \end{aligned} $$ ## Round to one decimal place $$ A \approx 680.9\text{ cm}^2 $$ $680.9\text{ cm}^2$ { "elements": [ { "type": "circle", "params": [[0, 0], 3.4], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 2, "fillColor": "rgba(140, 85, 242, 0.3)", "hasInnerPoints": true } }, { "type": "circle", "params": [[0, 0], 1.7], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 2, "fillColor": "#ffffff", "hasInnerPoints": true } }, { "type": "point", "params": [[0, 0]], "properties": { "name": "O", "color": "#583C87", "size": 3, "withLabel": true } }, { "type": "segment", "params": [[0, 0], [1.7, 0]], "properties": { "strokeColor": "#F2557F", "strokeWidth": 2, "name": "r", "withLabel": true, "labelPosition": [0.85, 0.2] } }, { "type": "segment", "params": [[0, 0], [0, 3.4]], "properties": { "strokeColor": "#5583F2", "strokeWidth": 2, "name": "R", "withLabel": true, "labelPosition": [-0.3, 1.7] } } ] } { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Annulus Area" ] }

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Explanation:

Identify the given radii and formula

Calculate the area of the annulus

Round to one decimal place

Answer: