Geometry help please!?

Question

two questions:

if a circle is inscribed in a square with the perimeter of 24 cm, what is the circumference of the circle?

if a circle with a circumference of 16(Pi) inches is circumscribed about a square, what is the legnth of a diagnol of the square?

if you can, please explaint hem to me..i dont want just the answers..i need an explanation so i can understand it.

thanks in advance =]

Answer 1

length of side of square: 6
diagonal of square : 6 rt 2
that's also the diameter of the circle, so

Circumfrence = 6pi rt 2

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Diagonal of square = diameter of circle. So divide by pi.

16.

Answer 2

A square with a perimeter of 24 cm means it has four sides of 6 cm. Hence the circle's diameter is the width of the square, and therefore 6 cm. The circumference of a circle is diameter * pi, hence the answer is:

6 pi.

If you draw a circle around a square the diagonal of the square is the diameter of the circle. (Draw it and you'll understand.) Reversing the logic of the first one, the you'll see the answer is 16 inches. This is because 16 pi inches is the circumference, and again, circumference is the diameter * pi.

Answer 3

You need to look at the diameter of the circle.

For the first question each side of the square would be 6cm, which means the diameter of the circle would also be 6cm because it goes from one side of the square to the other.

For the second question the diagonal of the square would be the same as the diameter of the circle, so work out the diameter from the circumference and you have the answer

Answer 4

Perimeter of the sqaure equals to 4 x length, 24cm divide by 4, you get 6cm, which means each side of the square is 6cm. And the circle is inscribed, which means the diameter is 6cm, because you find the end to end of the circletouching the side of square.

2nd question, circumference is 2(pi)r = 16Pi, 2r = 16 which is the diameter, because the corner of the square touch the circle.

Answer 5

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