find the volume of the cone.

diameter: 14 m, slant height: 25 m

round to the nearest whole number.

volume = ? $\text{m}^3$

Question

find the volume of the cone.

diameter: 14 m, slant height: 25 m

round to the nearest whole number.

volume = ? $\text{m}^3$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Pythagorean Theorem", "Volume of a Cone" ], "new_concepts": [], "current_concepts": [ "Pythagorean Theorem", "Volume of a Cone" ] } ## Find the radius of the cone base Using the *Volume of a Cone* knowledge point $$ r = \frac{d}{2} = \frac{14}{2} = 7\text{ m} $$ ## Calculate the vertical height of the cone Using the *Pythagorean Theorem* knowledge point $$ \begin{aligned} h^2 + r^2 &= l^2 \ h^2 + 7^2 &= 25^2 \ h^2 + 49 &= 625 \ h^2 &= 576 \ h &= 24\text{ m} \end{aligned} $$ ## Calculate the volume of the cone Using the *Volume of a Cone* knowledge point $$ \begin{aligned} V &= \frac{1}{3}\pi r^2 h \ V &= \frac{1}{3}\pi (7)^2 (24) \ V &= 8\pi (49) \ V &= 392\pi \ V &\approx 392 \times 3.14159265 \approx 1231.504\text{ m}^3 \end{aligned} $$ ## Round to the nearest whole number Using the *Volume of a Cone* knowledge point $$ V \approx 1232\text{ m}^3 $$ Find the volume of the cone. Diameter: 14 m, Slant Height: 25 m Round to the nearest whole number. Volume = 1232 $\text{m}^3$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Volume of a Cone" ] }

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QUESTION IMAGE

Question

Explanation:

Find the radius of the cone base

Calculate the vertical height of the cone

Calculate the volume of the cone

Round to the nearest whole number

Answer: