Find the radius of a circle with a central angle of pi/7 and a length of the intercepted arc equal to 7.7 cm. Round your answer to the nearest tenth.
angle*radius=arc
radius=7.7cm/(PI/7)=7.7*7cm/PI
check that.
I do want to point out that math teachers don't understand units and place value. "Round your answer to the nearest tenth"...what? cm, meter.
For instance, if you do that math...
answer: 17.1569029cm or 17.2cm or
0.171569029m or .2 m
Physics and chemistry teacher would agree, the problem should have stated
a) Round your answer to the nearest tenth cm, or
b) Round your answer to the nearest tenth meter, or
c) round your answer to two (or desired) significant digits.
Because the arc was measured to two significant digits (7.7cm), the answer could be nor more than two, or 17cm.
it says to find the radius
To find the radius of a circle with a central angle and the length of the intercepted arc, you can use the formula:
r = (s / θ)
where:
- r is the radius of the circle
- s is the length of the intercepted arc
- θ is the central angle in radians
In this case, the length of the intercepted arc is given as 7.7 cm, and the central angle is π/7 (pi/7 in radians).
Let's substitute these values into the formula:
r = (7.7 cm / π/7)
To divide by a fraction, you multiply by its reciprocal. So we can rewrite the expression as:
r = (7.7 cm * 7 / π)
Now, to find the value of r, we need to find the value of π. The value of pi (π) is approximately 3.14159.
r = (7.7 cm * 7 / 3.14159)
r = 17.35 cm / 3.14159
r ≈ 5.5142 cm
Rounding to the nearest tenth, the radius of the circle is approximately 5.5 cm.