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4 years ago

Find the circumference and area of the circle

Mathematics

1 answer:

ser-zykov [4K]4 years ago

5 0

Answer: C = 53.3 inches

A = 226.1 inches²

Step-by-step explanation:

The inscribed square has equal sides. To determine the hypotenuse of the square which is also the diameter of the circle, we would apply the Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

Hypotenuse² = 12² + 12² = 144 + 144 = 288

Hypotenuse = √288 = 16.97 inches

Radius = diameter/2 = 16.97/2 = 8.485 inches

The formula for determining the circumference of a circle is expressed as

Circumference = 2πr

Circumference = 2 × 3.14 × 8.485 = 53.3 inches

Area = πr²

Area = 3.14 × 8.485² = 226.1 inches²

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Answer:

$(x+1)^2 + (y- 3.5)^2 =64$

Step-by-step explanation:

We are given that endpoints of a diameter at the points (7,2) and (-9,5).

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So, first find the mid point of diameter

Formula : $x=\frac{x_1+x_2}{2} , y=\frac{y_1+y_2}{2}$

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Substitute the values in formula

$x=\frac{7-9}{2} , y=\frac{2+5}{2}$

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To find length of diameter :

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$(x_1,y_1)=(7,2)\\(y_1,y_2)=(-9,5)$

$d=\sqrt{(-9-7)^2+(5-2)^2}$

$d=\sqrt{265}$

Length of radius = r = $\frac{Diameter}{2}=\frac{\sqrt{256}}{2}$

Standard form of the equation of the circle : $(x -h)^2 + (y- k)^2 = r^2$

(h,k )=(-1,3.5)

$r=\frac{\sqrt{256}}{2}$

Equation of the circle : $(x+1)^2 + (y- 3.5)^2 =(\frac{\sqrt{256}}{2})^2$

Equation of the circle : $(x+1)^2 + (y- 3.5)^2 =64$

Hence the standard form of the equation of the circle with endpoints of a diameter at the points (7,2) and (-9,5) is $(x+1)^2 + (y- 3.5)^2 =64$

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