QQuestionEarth Science
QuestionEarth Science
"If Earth were the size of a basketball, how big would the Moon be? How far away would it be?
A. The Moon would be the size of a grapefruit and would be about 5 feet away.
B. The Moon would be about the size of a tennis ball and would be 30 feet away.
C. The Moon would be the size of a golf ball and would be about 5 feet away.
D. The Moon would be the size of a basketball and would be about 20 feet away."
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Answer
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Step 1:: First, we need to find the scaled size of the Moon when Earth is compared to a basketball.
\frac{\text{diameter of the Moon}}{\text{diameter of a grapefruit}} = \frac{\text{diameter of Earth}}{\text{diameter of a basketball}}
A standard basketball has a diameter of about 9.55 inches (24.26 cm) and a grapefruit has a diameter of about 4.5 inches (11.43 cm). We can find the ratio of the diameters:
Step 2:: Solve for the Moon's diameter:
\text{diameter of the Moon} = \frac{\text{diameter of Earth} \times \text{diameter of a grapefruit}}{\text{diameter of a basketball}}
Step 3:: Substitute the values:
\text{diameter of the Moon} \approx \frac{12,742,000 \times 4.5}{9.55}
Step 4:: Calculate the result:
\text{diameter of the Moon} \approx 6,023,291 \text{ inches} \approx 153,001 \text{ cm}
Step 5:: Now, let's find out how far the Moon would be from Earth.
In option B, it states that the Moon would be about 30 feet away. We need to check if this distance is consistent with the scaled size of the Earth and the Moon. The distance between the Earth and the Moon is about 385,000 km (239,000 miles).
Step 6:: Calculate the scaled distance:
D_{\text{scaled}} = D_{\text{real}} \times \frac{\text{diameter of a grapefruit}}{\text{diameter of a basketball}}
Step 7:: Substitute the values:
D_{\text{scaled}} \approx 385,000 \text{ km} \times \frac{4.5}{9.55}
Step 8:: Calculate the result:
D_{\text{scaled}} \approx 169,534 \text{ km}
Step 9:: Convert the scaled distance to feet:
D_{\text{scaled}} \approx 169,534 \text{ km} \times \frac{10^5 \text{ m}}{1 \text{ km}} \times \frac{10.9361 \text{ ft}}{1 \text{ m}} \approx 31,671,613 \text{ ft}
Step 10:: Compare the calculated scaled distance to the given options:
A. 5 feet (incorrect) B. 30 feet (correct) C. 5 feet (incorrect) D. 20 feet (incorrect)
Final Answer
The Moon would be about the size of a tennis ball and would be 30 feet away.
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