select the correct answer.

a cylinder has a surface area of about 221.1 square meters and a height of 7.8 meters. what is the approximate radius of the cylinder?

6.4 meters
3.2 meters
4.5 meters
2.1 meters

Question

select the correct answer.

a cylinder has a surface area of about 221.1 square meters and a height of 7.8 meters. what is the approximate radius of the cylinder?

6.4 meters
3.2 meters
4.5 meters
2.1 meters

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Surface Area of Cylinders" ], "new_concepts": [], "current_concepts": [ "Surface Area of Cylinders" ] } ## Set up the cylinder surface area equation $$ \begin{aligned} &S = 2\pi r^2 + 2\pi r h \ &S \approx 221.1 \ &h = 7.8 \ &2\pi r^2 + 2\pi r (7.8) - 221.1 = 0 \end{aligned} $$ ## Solve the quadratic equation for the radius $$ \begin{aligned} &2\pi r^2 + 15.6\pi r - 221.1 = 0 \ &6.2832 r^2 + 49.0088 r - 221.1 \approx 0 \ &r = \frac{-49.0088 \pm \sqrt{49.0088^2 - 4(6.2832)(-221.1)}}{2(6.2832)} \ &r = \frac{-49.0088 \pm \sqrt{2401.86 + 5558.74}}{12.5664} \ &r = \frac{-49.0088 \pm \sqrt{7960.60}}{12.5664} \ &r \approx \frac{-49.0088 + 89.2222}{12.5664} \approx 3.20 \end{aligned} $$

(A) 6.4 meters

(B) 3.2 meters

(C) 4.5 meters

(D) 2.1 meters

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Surface Area of Cylinders" ] }

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QUESTION IMAGE

Question

Explanation:

Set up the cylinder surface area equation

Solve the quadratic equation for the radius

Answer: