Find the circumference of a circle to the nearest tenth with the points (–10, –10) and(–3, 8) as the endpoints of a diameter. Round your answer to the nearest tenth.
The length of the diameter is √(7^2+18^2) = √373
so the radius is 1/2 √373
C = 2πr = √373 π
howw
To find the circumference of a circle, you need to know the length of its diameter.
Step 1: Find the distance between the two given points to find the diameter length.
Using the distance formula:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
d = √[(-3 - (-10))² + (8 - (-10))²]
= √[(7)² + (18)²]
= √[49 + 324]
= √[373]
≈ 19.3 (rounded to the nearest tenth)
Step 2: Use the diameter length to find the circumference of the circle.
The circumference (C) can be calculated using the formula: C = π * d, where π is approximately 3.14.
C = 3.14 * 19.3
≈ 60.6 (rounded to the nearest tenth)
Therefore, the circumference of the circle is approximately 60.6 units.
To find the circumference of a circle, you need to know the length of its diameter or radius. In this case, the problem gives you the endpoints of a diameter, which are (-10, -10) and (-3, 8).
The distance formula can be used to find the length of the diameter between these two points. The formula is:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Plugging in the values:
Distance = √[(-3 - (-10))^2 + (8 - (-10))^2]
= √[(-3 + 10)^2 + (8 + 10)^2]
= √[7^2 + 18^2]
= √[49 + 324]
= √373
≈ 19.3 (rounded to the nearest tenth)
Now that we have the diameter (19.3 units), we can find the circumference using the formula:
Circumference = π * diameter
Let's assume π (pi) is approximately 3.14:
Circumference = 3.14 * 19.3
≈ 60.6 (rounded to the nearest tenth)
Therefore, the circumference of the circle is approximately 60.6 units.