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2 years ago

The area of circle is 770cm^2then find its circumfrence

Mathematics

1 answer:

Gala2k [10]2 years ago

6 0

Answer:

The circumference is 98.39 centimeters (rounded to 2 decimal places)

Step-by-step explanation:

The area of a circle has the formula $\pi r^2$

The circumference of a circle has the formula $2\pi r$

First, let's find r from area given:

$\pi r^ 2= 770\\r^2 = \frac{770}{\pi}\\r=\sqrt{\frac{770}{\pi}} \\r=15.66$

Now, we can use this value of r and plug in into the formula for circumference. Shown below:

$2\pi (15.66)\\=98.39$

The circumference is 98.39 centimeters (rounded to 2 decimal places)

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skad [1K]

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$\vec s(u,v) = \left\langle 4 \cos(u) \sin(v), 4 \sin(u) \sin(v), 4 \cos(v) \right\rangle$

with 0 ≤ u ≤ π/2 and 0 ≤ v ≤ π/2.

Compute the outward-pointing normal vector to S :

$\vec n = \dfrac{\partial\vec s}{\partial v} \times \dfrac{\partial \vec s}{\partial u} = \left\langle 16 \cos(u) \sin^2(v), 16 \sin(u) \sin^2(v), 16 \cos(v) \sin(v) \right\rangle$

The integral of the field over S is then

$\displaystyle \iint_S \vec f \cdot d\vec s = \int_0^{\frac\pi2} \int_0^{\frac\pi2} \vec f(\vec s) \cdot \vec n \, du \, dv$

$\displaystyle = \int_0^{\frac\pi2} \int_0^{\frac\pi2} \left\langle 8 \cos(u) \sin(v), -12 \cos(v), 12 \sin(u) \sin(v) \right\rangle \cdot \vec n \, du \, dv$

$\displaystyle = 128 \int_0^{\frac\pi2} \int_0^{\frac\pi2} \cos^2(u) \sin^3(v) \, du \, dv = \boxed{\frac{64\pi}3}$

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1 year ago

The area of circle is 770cm^2then find its circumfrence​

The area of circle is 770cm^2then find its circumfrence