10th Class Mathematics Areas Related to Circles Question Bank Case Based (MCQs) - Areas Related to Circles

  • question_answer
    Find the total Length of the boundary of the region which is painted green.

    A) \[\text{128}\text{.57 cm}\]

    B) \[\text{132}.\text{56 cm}\]

    C) \[\text{145}.\text{57 cm}\]

    D) \[\text{15}0\text{ cm}\]

    Correct Answer: B

    Solution :

    Total length of boundary of region which is painted green = 4 [circumference of semi-circle of radius 4 cm each + length of arc of quadrant of radius 8 cm + radius of quadrant].
    \[=4\left[ \frac{1}{2}\times 2\pi (4)+\frac{1}{4}\times 2\times \pi \times 8+8 \right]\]
    \[=4[4\pi +4\pi +8]=4(8\pi +8)=4\left( 8\times \frac{22}{7}+8 \right)\]

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