Earth has a radius of about 6400 km, the Sun has a radius of about$ 7.0×10^5$ km, and a rubber ball has a radius of 6.4 cm. If you were to construct a scale model of the solar system using the rubber ball to represent Earth, what is the radius of a ball needed to represent the Sun in your model
A)$7.0 × 10^5$ cm
B)7.0 cm
C)700 cm
D)70 cm
E)7000 cm

Question

Quizplus · Accepted Answer

We need to use the ratio of the radii in order to find the radius of the Sun in the scale model:

\begin{align*}
\frac{	ext{radius of Sun}}{	ext{radius of Earth}} &= \frac{7.0	imes10^5	ext{ km}}{6400	ext{ km}}\
&=109.375
\end{align*}

This tells us that the radius of the Sun in the scale model needs to be 109.375 times larger than the radius of the Earth in the scale model. Since the radius of the rubber ball representing Earth is 6.4 cm, the radius of the ball representing the Sun in the scale model can be found by multiplying 6.4 cm by 109.375:

\begin{align*}
	ext{radius of Sun in scale model} &= 6.4	ext{ cm} 	imes 109.375\
&= 700	ext{ cm}
\end{align*}

Therefore, the best choice is C: 700 cm.

Earth Has a Radius of About 6400 Km, the Sun 7.0×105 7.0×10^57.0×105

Earth Has a Radius of About 6400 Km, the Sun $7.0×10^5$