Mercury has a radius of about 2500 km , the Sun has a radius of about 7.0times 10^5 km, and a rubber ball has a radius of 5 cm. If you were to construct a scale model of the Solar System using the rubber ball to represent Mercury,what is the radius of a ball needed to represent the Sun in your model? 7.0times 10^5cm 140 cm 1400 cm 7.0 cm

Here's how to solve this scale model problem:<br /><br />1. **Convert units:** Make sure all measurements are in the same units. Since the rubber ball's radius is given in cm, convert Mercury's and the Sun's radii to cm as well.<br /><br /> * Mercury's radius: 2500 km * 100,000 cm/km = 2.5 x 10^8 cm<br /> * Sun's radius: 7.0 x 10^5 km * 100,000 cm/km = 7.0 x 10^10 cm<br /><br />2. **Find the scale factor:** The scale factor is the ratio of the model size to the actual size. In this case, the rubber ball represents Mercury.<br /><br /> * Scale factor = (Radius of rubber ball) / (Radius of Mercury) = 5 cm / 2.5 x 10^8 cm = 2 x 10^-8<br /><br />3. **Calculate the model Sun's radius:** Multiply the Sun's actual radius by the scale factor to find the radius of the model Sun.<br /><br /> * Model Sun's radius = (Sun's radius) * (Scale factor) = 7.0 x 10^10 cm * 2 x 10^-8 = 1400 cm<br /><br />Therefore, the radius of the ball needed to represent the Sun in the model is $\boxed{1400 \text{ cm}}$.<br />