Question

The diagram shows a circle inside a semicircle.

Answer 1

A circle inside a semicircle is depicted in the diagram. The circle measures 10 cm in diameter. The semicircle has a 20 cm diameter. Calculate the shaded area. Give a precise response to the nearest decimal point.

The area of the shaded region is 39.3$cm^{2}$.

Given the diagram shows a circle inside a semicircle.

Every point in the plane of a circle, which is a closed, two-dimensional object, is evenly separated from the center. All lines that cross the circle join together to produce the line of reflection symmetry. Every angle also possesses rotational symmetry about its center.

Area of a circle = $\pi r^{2}$.

Semicircle is when a line travelling through the center of a circle reaches its two ends, a semicircle is created. Thus, a circle can be formed by combining two semicircles.

Area of a semicircle = $\frac{1}{2} \pi r^{2}$.

The circle has a diameter of 10 cm. The semicircle has a diameter of 20 cm.

Semicircle:

$r_{1}=\frac{d_{1} }{2}=\frac{20}{2}=10cm\\S_{1}=\frac{ \pi r_{1}^{2} }{2} =\frac{ \pi \times 10^{2} }{2} =50\pi cm^{2}$

Circle:

$r_{2}=\frac{d_{2} }{2}=\frac{10}{2}=5cm\\S_{2}=\pi r_{2}^{2} = \pi \times 5^{2} =25\pi cm^{2}$

So,

$S=\frac{S_{1} -S_{2}}{2} \\S=\frac{50\pi -25\pi}{2}\\S=\frac{25\pi}{2} \\S=39.3cm^{2}$

Therefore, The area of the shaded region is 39.3$cm^{2}$.

To learn more about semicircle visit: brainly.com/question/3442660

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