Math help. Please?

Question

Find the radius, diameter and circumference of a circle with an area of 64 pi cm2. Write your answers as decimals rounded to the nearest hundredth.

Find the circumference and area of a circle that has a rectangle inscribed inside it with sides that are 9 by 12 centimeters. Write your answer as decimals rounded to the nearest hundredth.

Okay.
I have the first one.
Now I need help on the second one.
Please and thank you!

Answer 1

The area is pi*r^2, sqrt(64) is 8, so radius is 8cm.
d=2r=16cm.
Circumference is pi*d=16pi cm = 50.27cm

You need to find the radius which is the distance from the center of the rectangle to a corner. This is the hypotenuse of a right triangle formed from the midpoint of one of the sides.

Use the pythagorean theorom to find the radius:

a^2 + b^2 = c^2

4.5^2 + 6^2 = r^2
r=sqrt(56.25)

area = pi*sqrt(56.25)^2
=56.25pi=176.71 cm^2

circumference = 2*pi*sqrt(56.25)
= 47.12 cm

Answer 2

The diagonal of the rectangle is the diameter of the circle

d = sqrt (9^2 + 12^2) = sqrt (225) = 15 cms

C = pi d = 47.12 cm
A = pi d^2/4 = 176.71 sq cms

Answer 3

2nd Question:
Assuming that all 4 corners of the rectangle touch the circle, you can find the diameter of the circle by splitting the rectangle in half and getting the length of the diagonal. Using the Pythagorean Theorem, the length of the diagonal is equal to sqrt(9^2 + 12^2) = 15 cm, . Since the diagonal splits the rectangle in half, it also splits the circle in half, thus giving you 15 cm as the diameter and 7.5 cm as the radius.

C = 2 * pi * r = 2 * 3.14 * 7.5 = 47.10 cm

A = pi * r^2 = 3.14 * 7.5 * 7.5 = 176.63 cm^2

Good luck.

Answer 4

Part I) A = pi r^2 = pi * 64
Cancel out the pi
A = r^2 = 64

Find radius: 64 ^ (1/2)
r = 8.00cm

D = 2r = 2*8.00 = 16.00cm

c = 2 pi r = 2 * pi * 8.00 = 50.3 cm

Part II) If the rectangle is 9 x 12 cm, the circle must have a diameter of 12 cm (r = 6 cm).

c = 2 pi r = 2 * pi * 6 = 37.7 cm
This part I am a little unsure of.

Answer 5

Area = Pi x Radius Squared.
64 pi cm² = pi x radius (remove pi from both sides)
64 cm² = radius (square root both sides)
8 cm = radius

Diameter = radius x 2 (substitute knowns)
Diameter = 8 cm x 2 (solve)
Diameter = 16 cm

Circumference = 2 x pi x radius (substitute knowns)
Circumference = 2 x pi x 8 cm (solve)
Circumference = 50.26548245 or 50.27 cm

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The distance from one corner of the square to the opposite corner is the same as the diameter.

Hypotenuse squared = side squared + side squared
Hypotenuse squared = 9 cm squared + 12 cm squared
Hypotenuse squared = 225 cm
Hypotenuse (or Diameter) = 15 cm

Circumference = pi x diameter
Circumference = 47.12388980 or 47.12 cm

Answer 6

r = √64 = 8 cm.
d = 2*8 = 16 cm.
C = 16π ≈ 50.26548245743669181540 cm.
which rounds to 50.27 cm.

Part 2
if the circle circumscribes a rectangle 9 x 12 cm, it must have the same diameter as the diagonal of the rectangle
√(9^2 + 12^2) = 15
C = 15π ≈ 47.12 cm
A = π (7.5)^2 ≈ 176.71 cm^2

Answer 7

Okay. Since area is (pi*radius^2), and area is 64*pi, then radius is 8 (sq rt. of 64). Diameter is 16 (2*radius), and circumference is pi*16. Pi starts at 3.14 for hundredths, so 50.24.

Answer 8

A = 64*pi = 200.96

A = r^2*pi = 200.96

r = 8 cm

d = 2r = 2*8 = 16 cm

C = pi * d = pi * 16 = 50.24 cm