Question

Geometry question, any help is appreciated

Answer 1

Volume ratio      250 : 686 = 125 : 343
Radius ratio       ∛(125) : ∛(343) = 5 : 7  scale factor
Area ratio           (5)² : (7)² = 25 : 49

Scale factor (5:7),  area ratio (25:49), volume ratio (125:343)

Answer 2

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 $V_{s}$ = 250 $yd^{3}$

Volume of large sphere $V_{l}$ = 686 $yd^{3}$.

Then the ratio of volume = 250 : 686 = 125 : 343.

Since, the volume of a sphere = $\frac{4 \pi \times r^{3}}{3}$, this gives us that the ratio of the radius = ∛$V_{s}$ : ∛$V_{l}$

i.e. The ratio of the radius = ∛125 : ∛343 = 5 : 7.

Further, as the surface area of a sphere = $4 \pi \times r^{2}$, this gives us that the ratioof surface area = $r_{s} ^{2}$ : $r_{l} ^{2}$

i.e The ratio of the surface area = $5^{2}$ : $7^{2}$ = 25 : 49

So, the ratio of the surface areas = 25 : 49.

Hence, the ratios are given by 5:7, 25:49, 125:343.