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 [tex]V_{s}[/tex] = 250 [tex]yd^{3}[/tex]
Volume of large sphere [tex]V_{l}[/tex] = 686 [tex]yd^{3}[/tex].
Then the ratio of volume = 250 : 686 = 125 : 343.
Since, the volume of a sphere = [tex]\frac{4 \pi \times r^{3}}{3}[/tex], this gives us that the ratio of the radius = ∛[tex]V_{s}[/tex] : ∛[tex]V_{l}[/tex]
i.e. The ratio of the radius = ∛125 : ∛343 = 5 : 7.
Further, as the surface area of a sphere = [tex]4 \pi \times r^{2}[/tex], this gives us that the ratioof surface area = [tex]r_{s} ^{2}[/tex] : [tex]r_{l} ^{2}[/tex]
i.e The ratio of the surface area = [tex]5^{2}[/tex] : [tex]7^{2}[/tex] = 25 : 49
So, the ratio of the surface areas = 25 : 49.
Hence, the ratios are given by 5:7, 25:49, 125:343.
