1Number 1ExplanationGeometry VisualizationLarge square, inscribed circle, and small square.LoadingToggle GridToggle Play If the area of the large square is 256 cm2256 \text{ cm}^2256 cm2, then the circumference of the circle is...7π cm7\pi\text{ cm}7π cm10π cm10\pi\text{ cm}10π cm12π cm12\pi\text{ cm}12π cm14π cm14\pi\text{ cm}14π cm16π cm16\pi\text{ cm}16π cmExplanationGiven the area of the large square is 256 cm2256 \text{ cm}^2256 cm2. Finding the Side Length of the Large Square The area of a square (AAA) is given by A=s2A = s^2A=s2. s2=256s^2 = 256s2=256s=256=16 cms = \sqrt{256} = 16 \text{ cm}s=256=16 cm Finding the Diameter of the Circle Notice that the circle is inscribed in the large square, tangent to its sides. Therefore, the diameter of the circle (ddd) is equal to the side length of the large square. d=s=16 cmd = s = 16 \text{ cm}d=s=16 cm Calculating the Circumference of the Circle The circumference of a circle (CCC) is given by C=πdC = \pi dC=πd. C=π⋅16=16π cmC = \pi \cdot 16 = 16\pi \text{ cm}C=π⋅16=16π cm Therefore, the circumference of the circle is 16π cm16\pi \text{ cm}16π cm.
1Number 1ExplanationGeometry VisualizationLarge square, inscribed circle, and small square.LoadingToggle GridToggle Play If the area of the large square is 256 cm2256 \text{ cm}^2256 cm2, then the circumference of the circle is...7π cm7\pi\text{ cm}7π cm10π cm10\pi\text{ cm}10π cm12π cm12\pi\text{ cm}12π cm14π cm14\pi\text{ cm}14π cm16π cm16\pi\text{ cm}16π cmExplanationGiven the area of the large square is 256 cm2256 \text{ cm}^2256 cm2. Finding the Side Length of the Large Square The area of a square (AAA) is given by A=s2A = s^2A=s2. s2=256s^2 = 256s2=256s=256=16 cms = \sqrt{256} = 16 \text{ cm}s=256=16 cm Finding the Diameter of the Circle Notice that the circle is inscribed in the large square, tangent to its sides. Therefore, the diameter of the circle (ddd) is equal to the side length of the large square. d=s=16 cmd = s = 16 \text{ cm}d=s=16 cm Calculating the Circumference of the Circle The circumference of a circle (CCC) is given by C=πdC = \pi dC=πd. C=π⋅16=16π cmC = \pi \cdot 16 = 16\pi \text{ cm}C=π⋅16=16π cm Therefore, the circumference of the circle is 16π cm16\pi \text{ cm}16π cm.
