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monitta
3 years ago
12

A square fits exactly inside a circle with each of the vertices being on the circumference of the circle. The square has sides l

ength of X cm. The area of the circle is 56cm^2. Work out the value of x. Give your answer correct to 3sf
Mathematics
1 answer:
NNADVOKAT [17]3 years ago
4 0

Answer: The value of x is 5.970.

Step-by-step explanation:

Given: The square has sides length of X cm.

Let r be the radius of the circle.

The square fits exactly inside a circle with each of the vertices being on the circumference of the circle.

Then diagonal of square = diameter of circle

i.e. \sqrt{2}x= 2r    [Diagonal of square = \sqrt{2}(side)]

i.e. r=\dfrac{x}{\sqrt{2}}

area of circle =\pi r^2

i.e. 56=\frac{22}{7}(\frac{x}{\sqrt{2}})^2

56=\frac{22}{7}\times\frac{x^2}{2}\\\\\Rightarrow\ x^2= \dfrac{7}{11}\times56\\\\\Rightarrow\ x^2=35.636\\\\\Rightarrow\ x=\sqrt{35.636}\approx5.970

Hence, the value of x is 5.970.

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the solution is here,

the coordinate of centre of circle A is (3,2)

and the coordinate of centre of circle B is (3,0).

so the translation point from A to B is (3-0,0-2)=(3,-2).

Now the translation rule is given by (x+h,y+k)

where h is the tranalation anlong the x-axis and k is the translation along the y-axis.

For this problem, translation ruleis (x+3,y-2).

Then, radius of circle A(r1)=2 units

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as the circle A is translated to B, the scale factor is

r2/r1=3/2=1.5

In conclusion, the translation rule for given circles is (x+3,y-2) and its scale factor is 1.5

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