Finding Ratio of two Sphere.

Question

Volume of Two Spheres are in the ratio 27:343 and the sum of their radius is 10. Find the ratio of the surface area of the bigger sphere to the smaller sphere.

Answer 1

V=(4/3)(∏)(r³) for a sphere  (notice the r to the 3rd power)

SA=(4)(∏)(r²) for a sphere   (notice the r to the 2nd power)

ratio of volumes is 27/343

find the cube root of 27 and the cube root of 343

the cube root of 27 is 3 and the cube root of 343 is 7

therefore the ratio of linear measures is 3:7

therefore the ratio of the surface areas is found by the squares of the linear measures

7²/3²=49/9 is the ratio of the surface areas (larger sphere to smaller sphere)