Question

the sun is approximately ten times the size of the planet jupiter.
if a basketball with a diameter of about 24 cm is used to represent the sun, which of the following should be used to represent jupiter?
a softball with a diameter of 8.9 cm
a golf ball with a diameter of 4.2 cm
a tennis ball with a diameter of 6.5 cm
a marble with a diameter of 2.5 cm

Explanation:

Step1: Set up the proportion

Let \( x \) be the diameter of the object representing Jupiter. Since the Sun is ten times Jupiter's size, we have the proportion \( \frac{\text{Sun's diameter}}{\text{Jupiter's diameter}}=\frac{10}{1} \). Given the Sun's - like object (basketball) has a diameter of \( 24\mathrm{cm} \), so \( \frac{24}{x}=\frac{10}{1} \).

Step2: Solve for \( x \)

Cross - multiply the proportion \( 10x = 24\times1 \). Then \( x=\frac{24}{10}=2.4\mathrm{cm} \). The marble with a diameter of \( 2.5\mathrm{cm} \) is the closest to \( 2.4\mathrm{cm} \).

Answer:

D. A marble with a diameter of \( 2.5\mathrm{cm} \)