Example Question - radius
Here are examples of questions we've helped users solve.
Calculating the Distance Traveled on a Circular Track
<p>La distancia recorrida es igual al perímetro de la pista (la circunferencia) multiplicado por el número de vueltas.</p> <p>La fórmula para calcular la circunferencia \( C \) es \( C = 2\pi r \), donde \( r \) es el radio.</p> <p>Dado que el radio \( r \) es de 62 metros y se dan 3 vueltas, la distancia \( D \) es:</p> <p>\( D = 2\pi r \times 3 \)</p> <p>\( D = 2\pi(62) \times 3 \)</p> <p>\( D = 2 \times 3.1416 \times 62 \times 3 \)</p> <p>\( D = 2 \times 3.1416 \times 186 \)</p> <p>\( D = 6.2832 \times 186 \)</p> <p>\( D = 1168.6752 \) metros</p> <p>Por lo tanto, la distancia recorrida es 1168.6752 metros.</p>
Completing a Logical Argument Involving Circle Geometry
Premis/Premise 1: <p>\text{Jika jejari sebuah bulatan ialah 7 cm, maka lilitan bulatan itu ialah 14x.}</p> <p>\text{If the radius of the circle is 7 cm, then the circumference of the circle is 14x.}</p> Premis/Premise 2: <p>\text{Untuk mencari lilitan sebuah bulatan, kita gunakan rumus } C = 2\pi r \text{.}</p> <p>\text{To find the circumference of a circle, we use the formula } C = 2\pi r \text{.}</p> Kesimpulan/Conclusion: <p>\text{Jejari bulatan itu bukan 7 cm.}</p> <p>\text{The radius of the circle is not 7 cm.}</p> Maka, Premis 2 harus menyatakan hubungan antara jejari dan lilitan dengan menggunakan formula yang betul supaya argumen logik ini sah. Premis 2 adalah: <p>\text{Oleh itu, jika jejari bulatan itu ialah 7 cm, kita boleh gunakan rumus } C = 2\pi r \text{ untuk mencari lilitannya, yang mana } C = 2\pi(7) = 14\pi \text{ cm, dan bukannya 14x.}</p> <p>\text{Therefore, if the radius of the circle is 7 cm, we can use the formula } C = 2\pi r \text{ to find its circumference, which is } C = 2\pi(7) = 14\pi \text{ cm, not 14x.}</p>
Solving for the Radius of a Circular Pond
<p>To solve for the radius of the circular pond, we can use the properties of triangles and circles. Since OB and OC are radii of the circle, they are equal. Triangle OBC is an isosceles triangle with OB = OC = radius (r), and BC = 88 m.</p> <p>Since AB and AC are tangents to the circle from the same external point A, AB = AC = 132 m.</p> <p>By the properties of tangents to a circle from a common external point, triangle ABC is also isosceles with AB = AC.</p> <p>Using the property that the tangents from an external point are equal, we get the lengths DA = DB and hence triangle ADB is also isosceles.</p> <p>Therefore, we can calculate the length of AD using the Pythagorean theorem for triangle ADB:</p> <p>\[ DB = AB - BD = 132 m - r \]</p> <p>\[ (AD)^2 + (DB)^2 = (AB)^2 \]</p> <p>\[ (AD)^2 + (132 - r)^2 = 132^2 \]</p> <p>Solve for \( AD \) in terms of \( r \):</p> <p>\[ AD = \sqrt{132^2 - (132 - r)^2} \]</p> <p>Now observe triangle OAD, it is a right triangle with OD perpendicular to AD.</p> <p>Applying the Pythagorean theorem:</p> <p>\[ OA^2 = OD^2 + AD^2 \]</p> <p>Since OA is the radius of the circle, we can substitute \( OA \) with \( r \), and \( OD \) with \( 88 \):</p> <p>\[ r^2 = 88^2 + (\sqrt{132^2 - (132 - r)^2})^2 \]</p> <p>Expand and simplify the equation:</p> <p>\[ r^2 = 88^2 + 132^2 - 2 \cdot 132 \cdot (132 - r) + (132 - r)^2 \]</p> <p>Further simplification gives us a quadratic equation in \( r \).</p> <p>Solve this quadratic equation to find the value of \( r \), which yields the radius of the circular pond.</p> <p>(Note: Due to incomplete information, the exact numerical value cannot be provided without the necessary steps to compile and simplify the equation.)</p>
Calculating the Area of a Circle
<p>Para encontrar el área \( A \) de un círculo, utilizamos la fórmula \( A = \pi r^2 \), donde \( r \) es el radio del círculo.</p> <p>En este caso, el radio \( r \) es de 5 cm. Sustituimos este valor en la fórmula:</p> <p>\( A = \pi \times 5^2 \)</p> <p>\( A = \pi \times 25 \)</p> <p>Por lo tanto, el área \( A \) del círculo es \( 25\pi \) cm\(^2\).</p>
Geometric Problem with Circle and Points
The image depicts a geometric problem involving a circle with points labeled A, B, C, D, and E, and a central point O. Some parts of the figure are labeled, such as AE as the diameter and OC as a radius measuring 2.5 cm. To give you a precise answer, I need to know the specific question you are looking to solve for this diagram. Could you please provide the question associated with this geometric figure?
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