Mathematical Methods — Question 7

QCAA 2022, Paper 1 · 1 mark

Q7 · 2022 · Technology-freeSimple familiar1 mark

QUESTION 7

A circle with radius

r

and internal angle

\theta

has a shaded segment as shown. If

\theta

is in radians, the area of the shaded segment is

(A)

\dfrac{r^2}{2}\left(\dfrac{\theta\pi}{180}-\sin\theta\right)

(B)

\dfrac{r^2}{2}(\theta-\sin\theta)

(C)

\dfrac{r^2}{4}\left(\dfrac{\theta\pi}{90}-1\right)

(D)

\dfrac{r^2}{2}(\theta-1)

ABCD

WORKED SOLUTION

1 mark

ANSWER

B —

\dfrac{r^2}{2}(\theta-\sin\theta)

Worked solution

The segment area is sector area minus triangle area:

\frac12r^2\theta-\frac12r^2\sin\theta=\frac{r^2}{2}(\theta-\sin\theta)

, so B.

Selects option B.

[1 mark]

Worked explanation by QCE Vault; correct option verified against the QCAA answer key.