Answer:
3
Step-by-step explanation:
Given: Sphere A and Sphere B are similar.
The volumes of A and B are 17 [tex]cm^3[/tex]and 136
The diameter of B is 6 cm.
To find: diameter of A
Solution:
Let R denotes radius of sphere A and r denotes radius of sphere B.
Radius of sphere A= R
Diameter of sphere B = 6 cm
So, radius of sphere B (r) = [tex]\frac{6}{2}=3\,\,cm[/tex]
Volume of sphere is [tex]\frac{4}{3}\pi(radius)^3[/tex]
Volume of sphere A = [tex]\frac{4}{3}\pi(R)^3[/tex]
[tex]\frac{\frac{4}{3}\pi R^3}{\frac{4}{3}\pi r^3}=\frac{17}{136}=\frac{1}{8}\\\frac{R^3}{r^3}=\frac{1}{8}\\\frac{R}{r}=\frac{1}{2}\\r=2R[/tex]
Put r = 3 cm
[tex]3=2R\\R=\frac{3}{2}=1.5\,\,cm[/tex]
Diameter of sphere A = 2 × Diameter
= 2 × 1.5
=3 cm
