Final answer:
To find the apex angle of the remaining portion of the pie, one must subtract the angles of the eaten pieces from the total angle in radians of the circle (2π). Since the arc length equals the radius, the apex angle of each piece, therefore, is 1 radian. However, options given appear to require re-evaluation as none matches '1 radian,' which indicates a possible misunderstanding in the question.
Step-by-step explanation:
The student is asking about finding the apex angle in radians of the remaining portion of a pie after certain wedge-shaped pieces have been removed. To solve this, we need to understand that the arc length (a) along the outer crust of each piece is given to be equal to the radius (r) of the pie. Since the formula for arc length is a = rθ, where θ is the central angle in radians, and given a = r, we can deduce that θ = 1 radian.
For a full circle, the rotation angle is 2π radians as the arc length is equal to the circumference of the circle, which is 2πr. Each piece removed is a slice of this full rotation. If the entire pie was eaten in this way, each piece would have an arc of length equal to the radius, or 1 radian per piece.
To find the apex angle of the remaining portion, we need to subtract the radians of the eaten pieces from the total radians in a circle (2π). If every piece eaten has an angle of 1 radian, and the whole pie has 2π radians, the remaining portion after one such piece is eaten would be 2π - 1 radians. To conclude, we must calculate this value and match it with the closest option.
2π - 1 = 6.283 - 1 ≈ 5.283 radians. However, this doesn't match any of the options provided. Upon re-evaluation, we realize an apex angle refers to the angle for a single piece, not the entire remaining portion. Therefore, the apex angle we are looking for is simply 1 radian.