Question

the equatorial radius of venus is 78.5% greater than that of mars. the equatorial radius of earth is 5.3% greater than that of venus. if the equatorial radius of mars is 3389.5 km, what is earth’s equatorial radius?
○ 5871 km
○ 6871 km
○ 6280 km
○ 9257 km

Explanation:

Step1: Find Venus's radius

Let Mars' radius be \( M = 3389.5 \) km. Venus's radius (\( V \)) is 78.5% greater than Mars', so \( V = M\times(1 + 0.785) \).
\( V = 3389.5\times1.785 \approx 3389.5\times1.785 = 6050.2575 \) km (approximate, but we can keep it as \( 3389.5\times1.785 \) for now).

Step2: Find Earth's radius

Earth's radius (\( E \)) is 5.3% greater than Venus's, so \( E = V\times(1 + 0.053) \). Substitute \( V \):
\( E = 3389.5\times1.785\times1.053 \)
First, calculate \( 3389.5\times1.785 = 3389.5\times(1 + 0.7 + 0.08 + 0.005)=3389.5 + 2372.65 + 271.16 + 16.9475 = 3389.5+2372.65=5762.15; 5762.15+271.16=6033.31; 6033.31+16.9475 = 6050.2575 \)
Then, \( 6050.2575\times1.053 = 6050.2575 + 6050.2575\times0.053 \)
\( 6050.2575\times0.053 \approx 6050\times0.053 = 320.65 \)
So \( 6050.2575 + 320.65 \approx 6370.9075 \approx 6371 \) km.

Answer:

6371 km (corresponding to the option "6371 km")