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", "quick" ], "needs_drawing": false, "concepts_used": [ "Surface Area of a Cone", "Pythagorean Theorem" ], "new_concepts": [], "current_concepts": [ "Surface Area of a Cone", "Pythagorean Theorem" ] } ## Identify given values $$ \begin{aligned} h &= 24\text{ cm} \ r &= 18\text{ cm} \end{aligned} $$ ## Calculate slant height $$ \begin{aligned} l &= \sqrt{r^2 + h^2} \ l &= \sqrt{18^2 + 24^2} \ l &= \sqrt{324 + 576} \ l &= \sqrt{900} \ l &= 30\text{ cm} \end{aligned} $$ ## Calculate total surface area $$ \begin{aligned} \text{SA} &= \pi r l + \pi r^2 \ \text{SA} &= \pi (18)(30) + \pi (18)^2 \ \text{SA} &= 540\pi + 324\pi \ \text{SA} &= 864\pi\text{ cm}^2 \end{aligned} $$ Find the surface area of the cone below. Leave your answer in terms of $\pi$. $\text{SA} =$ 864 $\pi\text{ cm}^2$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Surface Area of a Cone" ] }

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Question

Explanation:

Identify given values

Calculate slant height

Calculate total surface area

Answer: