Find the length of an arc of a circle whose central angle is 135 and radius is 8 cm. Round your answer to the nearest tenth.
Oh, calculating the length of an arc? Sure thing! Let me grab my measuring tape... Oh, wait. I've got a better idea!
So, the length of an arc is calculated using the formula L = 2πrθ/360, where L is the length of the arc, r is the radius, and θ is the central angle.
In this case, the radius is 8 cm and the central angle is 135 degrees. Plugging those values into the formula, we get L = (2π * 8 * 135) / 360.
Doing the math, we find that the length of the arc is approximately 30.0 cm. So, the answer is 30.0 cm, rounded to the nearest tenth. Voila!
To find the length of an arc of a circle, you can use the formula:
Length of Arc = (Central Angle / 360) * 2 * π * Radius
Let's substitute the given values into the formula:
Length of Arc = (135 / 360) * 2 * π * 8
Simplifying:
Length of Arc = (0.375) * 2 * π * 8
Length of Arc = 3 * π * 8
Using 3.14 as an approximation for π:
Length of Arc ≈ 3 * 3.14 * 8
Length of Arc ≈ 75.36 cm
Rounding to the nearest tenth:
Length of Arc ≈ 75.4 cm
Therefore, the length of the arc is approximately 75.4 cm.
To find the length of an arc, you can use the formula:
Length of Arc = (Central Angle / 360°) x (2πr)
where:
- Central Angle is the measure of the angle formed at the center of the circle,
- r is the radius of the circle,
- 2π is a constant value representing the circumference of a circle.
Now, let's plug in the given values into the formula:
Length of Arc = (135° / 360°) x (2π x 8 cm)
Simplifying further:
Length of Arc = (0.375) x (16π cm)
To round your answer to the nearest tenth, we can calculate the value. First, multiply 0.375 by 16π, which is approximately 50.265483 cm. Rounding this value to the nearest tenth, we get 50.3 cm (rounded to one decimal place).
Therefore, the length of the arc is approximately 50.3 cm (rounded to the nearest tenth).
Here, when someone asks a question, does he get the answer on time???
i need to know?
The whole circle would have a circumference of 16π cm
you want 135/360 or 3/8 of that
arc = (3/8)(16π) cm
= 6π cm