a company produces individually wrapped spherical cookies. the minimum amount of wrapping material needed to cover a cookie, assuming no edges overlap, is 314 square inches. what is the diameter of one cookie? (use 3.14 for the value of $\pi$.)

5 in.
10 in.
20 in.
25 in.

Question

a company produces individually wrapped spherical cookies. the minimum amount of wrapping material needed to cover a cookie, assuming no edges overlap, is 314 square inches. what is the diameter of one cookie? (use 3.14 for the value of \$\pi\$.)

5 in.
10 in.
20 in.
25 in.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Surface Area of a Sphere", "Sphere Diameter" ], "current_concepts": [ "Surface Area of a Sphere", "Sphere Diameter" ] } ## Set up the surface area equation for a sphere $$ \begin{aligned} A &= 4\pi r^2 \ 314 &= 4(3.14)r^2 \end{aligned} $$ ## Solve for the radius $$ \begin{aligned} 314 &= 12.56r^2 \ r^2 &= \frac{314}{12.56} \ r^2 &= 25 \ r &= 5 \end{aligned} $$ ## Calculate the diameter $$ \begin{aligned} d &= 2r \ d &= 2(5) \ d &= 10\text{ in.} \end{aligned} $$

5 in.

10 in.

20 in.

25 in.

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

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QUESTION IMAGE

Question

Explanation:

Set up the surface area equation for a sphere

Solve for the radius

Calculate the diameter

Answer: