Example Question - calculate circumference
Here are examples of questions we've helped users solve.
Calculating the Circumference of a Cylinder's Base
<p>The volume \( V \) of a cylinder is given by \( V = \pi r^2 h \) where \( r \) is the radius and \( h \) is the height. </p> <p>Given:</p> <p>\( V = 12,936 \text{ cm}^3 \)</p> <p>\( h = 21 \text{ cm} \)</p> <p>\( \pi \approx \frac{22}{7} \)</p> <p>To find the circumference \( C \), we need to find the radius \( r \) first.</p> <p>From the volume formula:</p> <p>\( 12,936 = \frac{22}{7} \times r^2 \times 21 \)</p> <p>Solving for \( r^2 \):</p> <p>\( r^2 = \frac{12,936 \times 7}{22 \times 21} \)</p> <p>\( r^2 = \frac{12,936}{66} \)</p> <p>\( r^2 = 196 \)</p> <p>\( r = \sqrt{196} \)</p> <p>\( r = 14 \text{ cm} \)</p> <p>Now we calculate the circumference \( C \) using the radius \( r \):</p> <p>\( C = 2 \pi r \)</p> <p>\( C = 2 \times \frac{22}{7} \times 14 \)</p> <p>\( C = 88 \text{ cm} \)</p> <p>Therefore, the circumference of the base of the cylinder is \( 88 \text{ cm} \).</p>
Calculate Circumference of Circle from Given Area
The question in the image asks for the circumference of a circle whose area is 49 m². To find the circumference, we first need to determine the radius of the circle. The formula for the area of a circle is: \[ A = \pi r^2 \] where \( A \) is the area and \( r \) is the radius. Given that the area \( A \) is 49 m², we can solve for \( r \) as follows: \[ 49 = \pi r^2 \] Divide both sides by \( \pi \) to get: \[ \frac{49}{\pi} = r^2 \] Take the square root of both sides to solve for \( r \): \[ r = \sqrt{\frac{49}{\pi}} = \frac{\sqrt{49}}{\sqrt{\pi}} = \frac{7}{\sqrt{\pi}} \] Now we have the radius. The circumference \( C \) of a circle is given by the formula: \[ C = 2\pi r \] We can substitute \( r = \frac{7}{\sqrt{\pi}} \) into this formula to find the circumference: \[ C = 2\pi\left(\frac{7}{\sqrt{\pi}}\right) \] Now let's simplify: \[ C = \frac{14\pi}{\sqrt{\pi}} \] Multiplying the top and bottom by \( \sqrt{\pi} \) to rationalize the denominator, we get: \[ C = \frac{14\pi\sqrt{\pi}}{\pi} = 14\sqrt{\pi} \] Finally, you can leave the answer in terms of \( \pi \) as the question requests. The circumference \( C \) is: \[ C = 14\sqrt{\pi} \: \text{meters} \]
Calculating Circumference of a Circle from Area
The question asks for the circumference of a circle given its area. The area (A) of a circle is related to its radius (r) by the formula: \[ A = \pi r^2 \] Given that the area is 36π cm², we can set up the equation: \[ 36\pi = \pi r^2 \] We can solve for r by dividing both sides of the equation by π: \[ 36 = r^2 \] Taking the square root of both sides gives us: \[ r = \sqrt{36} \] \[ r = 6 \text{ cm} \] The circumference (C) of a circle is related to the radius by the formula: \[ C = 2\pi r \] Substituting the radius we found into the circumference formula gives us: \[ C = 2\pi \times 6 \] \[ C = 12\pi \] So the circumference of the circle is 12π centimeters.
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