To determine the factor by which the radius of sphere A is multiplied to produce the radius of sphere B, follow these steps:
1. Identify the radius of sphere A:
- The radius of sphere A is given as 24 centimeters.
2. Determine the radius of sphere B:
- The diameter of sphere B is given as 42 centimeters.
- Since the radius is half the diameter, calculate the radius of sphere B:
[tex]\[
\text{Radius of sphere B} = \frac{\text{Diameter of sphere B}}{2} = \frac{42 \text{ cm}}{2} = 21 \text{ cm}
\][/tex]
3. Calculate the multiplication factor:
- We need to determine by what factor the radius of sphere A (24 cm) is multiplied to obtain the radius of sphere B (21 cm).
- This factor is found by dividing the radius of sphere B by the radius of sphere A:
[tex]\[
\text{Factor} = \frac{\text{Radius of sphere B}}{\text{Radius of sphere A}} = \frac{21 \text{ cm}}{24 \text{ cm}}
\][/tex]
4. Simplify the fraction:
- Simplify the fraction [tex]\(\frac{21}{24}\)[/tex]:
[tex]\[
\frac{21}{24} = \frac{21 \div 3}{24 \div 3} = \frac{7}{8}
\][/tex]
Therefore, 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]\(\boxed{\frac{7}{8}}\)[/tex].
