Let's break down the solution step by step to figure out the multiplying factor:
1. Identify the given information:
- Sphere A has a radius of 24 centimeters.
- Sphere B has a diameter of 42 centimeters.
2. Calculate the radius of Sphere B:
Since the diameter is twice the radius, we can find the radius of sphere B by dividing its diameter by 2:
[tex]\[
\text{radius of Sphere B} = \frac{\text{diameter of Sphere B}}{2} = \frac{42}{2} = 21 \text{ centimeters}
\][/tex]
3. Determine the multiplying factor:
We need to find the factor by which the radius of Sphere A is multiplied to get the radius of Sphere B. This can be calculated as:
[tex]\[
\text{factor} = \frac{\text{radius of Sphere B}}{\text{radius of Sphere A}} = \frac{21}{24}
\][/tex]
4. Simplify the fraction:
Simplify [tex]\(\frac{21}{24}\)[/tex] to its lowest terms:
[tex]\[
\frac{21}{24} = \frac{7 \cdot 3}{8 \cdot 3} = \frac{7}{8}
\][/tex]
Thus, the radius of Sphere A is multiplied by [tex]\(\frac{7}{8}\)[/tex] to produce the radius of Sphere B. Therefore, the correct answer is:
[tex]\[
\boxed{\frac{7}{8}}
\][/tex]
