Question

both circles have the same center. what is the area of the shaded region?
d=46 cm
50 cm
write your answer as a whole number or a decimal rounded to the nearest hundredth.
square centimeters
submit
work it out
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Explanation:

Step1: Find radius of inner circle

The diameter of the inner circle \( d = 46 \) cm, so radius \( r=\frac{d}{2}=\frac{46}{2} = 23 \) cm.

Step2: Area of outer circle

Radius of outer circle \( R = 50 \) cm. Area of outer circle \( A_{outer}=\pi R^{2}=\pi\times50^{2}=2500\pi \) \( cm^{2} \).

Step3: Area of inner circle

Area of inner circle \( A_{inner}=\pi r^{2}=\pi\times23^{2}=529\pi \) \( cm^{2} \).

Step4: Area of shaded region

Shaded area \( = A_{outer}-A_{inner}=2500\pi - 529\pi=(2500 - 529)\pi=1971\pi \). Calculate \( 1971\times3.14159265\approx1971\times3.14 = 6188.94 \) (rounded to nearest hundredth).

Answer:

\( 6188.94 \)