Question

A ˚le has a radius of 14cm. Find the length (s) of the arc intercepted by a central angle of 3pi/2 radians.

A. (21) cm
B. (28) cm
C. (35) cm
D. (42) cm

Answer 1

The length (s) of the arc intercepted by a central angle of 3pi/2 radians is 66 cm. None of the provided options are correct.

Step-by-step explanation:

To find the length of the arc intercepted by a central angle in a circle, we use the formula for arc length which is
`\( s = r \cdot \theta \)`, where
`\( s \)` is the arc length,
`\( r \)`is the radius of the circle, and
`\( \theta \)`is the central angle in radians.

In this case, we are given that the radius of the circle
`(\( r \))` is 14 cm and the central angle
`(\( \theta \))` is
`\( (3\pi)/(2) \)` radians.

Now we will compute the length of the arc
`(\( s \))`using these values:


`\[ s = r \cdot \theta \]`

`\[ s = 14 \text{ cm} \cdot (3\pi)/(2) \]`

Multiplying the radius by the central angle gives us the arc length:


`\[ s = 14 \cdot (3\pi)/(2) \]`

`\[ s = 7 \cdot 3\pi \]`

`\[ s = 21\pi \text{ cm} \]`

The value of
`\( s \)` is approximately 3.14159. When we multiply 21 by
`\( \pi \)`, we will get a non-integer value. Given the correct answer calculated earlier is approximately
`\( 65.97344572538566 \)` cm, and since we are asked for a whole number, we can round this to the nearest whole number, which is 66 cm.

The correct answer is not explicitly listed in the given options A, B, C, and D.