To determine the factor by which the radius of sphere A is multiplied to obtain the radius of sphere B, follow these steps:
1. Determine the radius of sphere B:
- Given: The diameter of sphere B is 42 centimeters.
- The radius is half of the diameter. Therefore, the radius of sphere B is:
[tex]\[
\text{radius}_{B} = \frac{\text{diameter}_{B}}{2} = \frac{42}{2} = 21 \text{ cm}
\][/tex]
2. Use the radius of sphere A to find the multiplication factor:
- Given: The radius of sphere A is 24 centimeters.
- We need to find the factor by which the radius of sphere A is multiplied to get the radius of sphere B, which can be done by dividing the radius of sphere B by the radius of sphere A:
[tex]\[
\text{factor} = \frac{\text{radius}_{B}}{\text{radius}_{A}} = \frac{21}{24}
\][/tex]
3. Simplify the fraction to find the exact factor:
- To simplify [tex]\(\frac{21}{24}\)[/tex], divide both the numerator and the denominator by their greatest common divisor (GCD), which is 3:
[tex]\[
\frac{21 \div 3}{24 \div 3} = \frac{7}{8}
\][/tex]
Thus, the radius of sphere A is multiplied by [tex]\(\frac{7}{8}\)[/tex] to produce the radius of sphere B.
The correct answer is:
[tex]\(\frac{7}{8}\)[/tex]
