What is the area of the larger part of the…

What is the area of the larger part of the circle, to the left of x = 3?

Question 38

MediumOriginal question

The circle $x^{2} + y^{2} = 25$ is cut by the line $x = 3$ into a smaller and a larger part.

What is the area of the larger part of the circle, to the left of $x = 3$ ?

- 25 \sin^{-1}{\left(\frac{3}{5} \right)} - 12 + \frac{25 \pi}{2}

square unitsCorrect answerYour answer

12 + 25 \sin^{-1}{\left(\frac{3}{5} \right)} + \frac{25 \pi}{2}

square unitsCorrect answerYour answer

25 \pi

square unitsCorrect answerYour answer

- 25 \sin^{-1}{\left(\frac{3}{5} \right)} - 12 + \frac{75 \pi}{2}

square unitsCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Larger part = whole circle − smaller part.
$25\pi - (- 25 \sin^{-1}{\left(\frac{3}{5} \right)} - 12 + \frac{25 \pi}{2}) = 12 + 25 \sin^{-1}{\left(\frac{3}{5} \right)} + \frac{25 \pi}{2}$ .

Worth noting

Adding the smaller part goes past the whole circle.

Ten questions from Area of Bounded Regions, at your own pace.

Ten questions from Area of Bounded Regions, at your own pace.