find the surface area of the cone below.
leave your answer in terms of $\pi$.

$sa = ? \pi\text{ cm}^2$

Question

find the surface area of the cone below.
leave your answer in terms of $\pi$.

$sa = ? \pi\text{ cm}^2$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Pythagorean Theorem", "Surface Area of a Cone" ], "new_concepts": [], "current_concepts": [ "Pythagorean Theorem", "Surface Area of a Cone" ] } ## Find the slant height of the cone Using the **Pythagorean Theorem** knowledge point $$ \begin{aligned} &l^2 = 20^2 + 15^2\ &l^2 = 400 + 225 = 625\ &l = \sqrt{625} = 25\text{ cm} \end{aligned} $$ ## Calculate the surface area of the cone Using the **Surface Area of a Cone** knowledge point $$ \begin{aligned} &\text{SA} = \pi r l + \pi r^2\ &\text{SA} = \pi (15)(25) + \pi (15)^2\ &\text{SA} = 375\pi + 225\pi = 600\pi\text{ cm}^2 \end{aligned} $$ Find the surface area of the cone below. Leave your answer in terms of $\pi$. $\text{SA} =$ $600$$\pi\text{ cm}^2$ { "elements": [ { "type": "point", "params": [[0, -3]], "properties": { "name": "Center", "size": 3, "color": "#583C87", "withLabel": false } }, { "type": "point", "params": [[0, 4]], "properties": { "name": "Apex", "size": 3, "color": "#583C87", "withLabel": false } }, { "type": "point", "params": [[3.5, -3]], "properties": { "name": "Edge", "size": 3, "color": "#583C87", "withLabel": false } }, { "type": "ellipse", "params": [[0, -3], 3.5, 1.0], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 2, "fillColor": "rgba(140, 85, 242, 0.1)" } }, { "type": "segment", "params": [[0, 4], [-3.5, -3]], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 2 } }, { "type": "segment", "params": [[0, 4], [3.5, -3]], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 2 } }, { "type": "segment", "params": [[0, 4], [0, -3]], "properties": { "strokeColor": "#5583F2", "strokeWidth": 2, "dash": 2 } }, { "type": "segment", "params": [[0, -3], [3.5, -3]], "properties": { "strokeColor": "#5583F2", "strokeWidth": 2, "dash": 2 } }, { "type": "text", "params": [-0.8, 0.5, "20 cm"], "properties": { "color": "#583C87" } }, { "type": "text", "params": [1.5, -3.4, "15 cm"], "properties": { "color": "#583C87" } }, { "type": "text", "params": [2.0, 0.8, "l = 25 cm"], "properties": { "color": "#8C55F2" } } ] } { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Surface Area of a Cone" ] }

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Question

Explanation:

Find the slant height of the cone

Calculate the surface area of the cone

Answer: