Answer:
Hence, the ratios are given by 5:7, 25:49, 125:343.
Step-by-step explanation:
We are given two spheres such that:
Volume of small sphere
= 250 ![yd^{3}](https://tex.z-dn.net/?f=yd%5E%7B3%7D)
Volume of large sphere
= 686
.
Then the ratio of volume = 250 : 686 = 125 : 343.
Since, the volume of a sphere =
, this gives us that the ratio of the radius = ∛
: ∛![V_{l}](https://tex.z-dn.net/?f=V_%7Bl%7D)
i.e. The ratio of the radius = ∛125 : ∛343 = 5 : 7.
Further, as the surface area of a sphere =
, this gives us that the ratioof surface area =
: ![r_{l} ^{2}](https://tex.z-dn.net/?f=r_%7Bl%7D%20%5E%7B2%7D)
i.e The ratio of the surface area =
:
= 25 : 49
So, the ratio of the surface areas = 25 : 49.
Hence, the ratios are given by 5:7, 25:49, 125:343.