a cone has a circular base with a diameter of 18 inches. the height of the cone is 40 inches.

what is the approximate lateral area of the cone? use 3.14 for $\pi$ and round to the nearest whole number.

565 square inches
580 square inches
1,131 square inches
1,159 square inches

Question

a cone has a circular base with a diameter of 18 inches. the height of the cone is 40 inches.

what is the approximate lateral area of the cone? use 3.14 for $\pi$ and round to the nearest whole number.

565 square inches
580 square inches
1,131 square inches
1,159 square inches

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Pythagorean Theorem" ], "new_concepts": [ "Lateral Area of a Cone", "Slant Height of a Cone" ], "current_concepts": [ "Pythagorean Theorem", "Lateral Area of a Cone", "Slant Height of a Cone" ] } ## Calculate the radius and slant height of the cone $$ \begin{aligned} r &= \frac{d}{2} = \frac{18}{2} = 9\text{ inches} \ l &= \sqrt{r^2 + h^2} = \sqrt{9^2 + 40^2} = \sqrt{81 + 1600} = \sqrt{1681} = 41\text{ inches} \end{aligned} $$ ## Calculate the lateral area of the cone $$ \begin{aligned} L &= \pi r l \ L &\approx 3.14 \times 9 \times 41 \ L &\approx 3.14 \times 369 = 1158.66\text{ square inches} \ L &\approx 1159\text{ square inches} \end{aligned} $$

(A) 565 square inches

(B) 580 square inches

(C) 1,131 square inches

(D) 1,159 square inches

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

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QUESTION IMAGE

Question

Explanation:

Calculate the radius and slant height of the cone

Calculate the lateral area of the cone

Answer: