Question

Sphere 1 has surface area a1 and volume v1 and sphere 2 has surface area a2 and volume v2. if the radius of sphere 2 is 2.71 times the radius of sphere 1, what is the ratio of the areas a2/a1?

Answer 1

To find the ratio of the surface areas a2/a1, substitute the given radius values into the formula for the surface area of a sphere and simplify the expression. The ratio of the surface areas a2/a1 is 6.785.

Step-by-step explanation:

To find the ratio of the surface areas a2/a1, we need to find the formulas for the surface area of spheres with radius r and 2.71r. The formula for the surface area of a sphere is 4πr^2. So, the surface area of sphere 1 is 4πr1^2 and the surface area of sphere 2 is 4πr2^2.

Substituting 2.71r for r1 and 2.71r*2.71r for r2 in the formulas, we get:

Surface area of sphere 1 (a1) = 4π(2.71r)^2 = 4π*7.3641r^2 = 29.4564πr^2

Surface area of sphere 2 (a2) = 4π(2.71r*2.71r)^2 = 4π*7.3641*7.3641*r^2 = 199.8681554πr^2

Therefore, the ratio of the surface areas a2/a1 = 199.8681554πr^2 / 29.4564πr^2 = 6.785.

Answer 2

The surface area of a sphere is given by the equation AS = 4π * r ^ 2. For this formula, r equals the radius of the sphere
We have then that
a1 = 4π * r1 ^ 2
a2 = 4π * r2 ^ 2
r2 = 2.71r1
Then, dividing the areas
a2 / a1 = (4π * (2.71r1) ^ 2) / (4π * r1 ^ 2) = (7.3441 / 1) * (r1 ^ 2 / r1 ^ 2) = 7.3441
answer
the ratio of the areas a2 / a1 is 7.3441