Answer:
The ratio of the volume of the larger sphere to the volume of the smaller sphere is
2352637 : 1
Step-by-step explanation:
Volume of a sphere is
[tex] \frac{4}{3} \pi {r}^{3} [/tex]
Where r is the radius
radius = diameter / 2
For First sphere
diameter = 8yards
radius = 8 / 2 = 4 yards
Volume of first sphere is
[tex] \frac{4}{3} \pi( {4})^{3} \\ \\ = \frac{256}{3} \pi \: {yd}^{3} [/tex]
For second sphere
diameter = 1064 yards
radius = 1064 / 2 = 532 yards
Volume of second sphere is
[tex] \frac{4}{3} \pi( {532})^{3} \\ \\ = \frac{602275072}{3} \pi \: {yd}^{3} [/tex]
Since the volume of the second sphere is the largest
Ratio of the second sphere to the first one is
[tex] \frac{602275072}{3} \pi \div \frac{256}{3} \pi \\ \\ = \frac{602275072}{3} \pi \times \frac{3}{256} \pi \\ \\ = \frac{602275072}{256} \\ \\ = \frac{ 2352637}{1} \\ \\ = 2352637: 1[/tex]
Hope this helps you
