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 3.53 times the radius of sphere 1, what is the ratio of the areas A2/A1 ?

1.25×101 & 4.40×101 are correct answers but i dont remember how i got them

the ratio of the areas is the square of the ratio of the radii

To find the ratio of the areas A2/A1, we can use the formula for the surface area of a sphere, which is given by:

A = 4πr^2

Let's assume the radius of sphere 1 is r1 and the radius of sphere 2 is r2. We are given that r2 = 3.53 * r1.

For sphere 1:
Surface area A1 = 4πr1^2

For sphere 2:
Surface area A2 = 4πr2^2

Substituting r2 = 3.53 * r1 into the equation for A2, we get:
A2 = 4π(3.53 * r1)^2
A2 = 4π * (3.53^2 * r1^2)
A2 = 4π * 12.4609 * r1^2
A2 ≈ 49.8434 * π * r1^2

Now we can find the ratio of A2/A1:
A2/A1 = (49.8434 * π * r1^2) / (4πr1^2)
A2/A1 = 49.8434 / 4
A2/A1 ≈ 12.4609

Therefore, the ratio of the areas A2/A1 is approximately 12.4609.

To find the ratio of the areas A2/A1, we can use the formula for the surface area of a sphere, which is given by A = 4πr^2, where A is the surface area and r is the radius.

Let's first find the ratio of the volumes V2/V1.
We know that the volume of a sphere is given by V = (4/3)πr^3.

Since the radius of sphere 2 is 3.53 times the radius of sphere 1, we can write r2 = 3.53 * r1.

To find the ratio of the volumes, we substitute the values into the formula:
(V2/V1) = [(4/3)πr2^3] / [(4/3)πr1^3]
(V2/V1) = (r2^3) / (r1^3)
(V2/V1) = (3.53 * r1)^3 / r1^3
(V2/V1) = (3.53^3) * (r1^3) / (r1^3)
(V2/V1) = (3.53^3)

Now, let's find the ratio of the areas A2/A1.
Since we have the ratio of the volumes, we can use the fact that the ratio of the surface areas of two spheres is equal to the square of the ratio of their volumes.

(A2/A1) = [(V2/V1)^2] = [(3.53^3)^2] = (3.53^6)

To simplify the calculation, we can use a calculator or a scientific notation. The result is approximately 125.04 (rounded to two decimal places), which is equivalent to 1.25×10^2 in scientific notation.

Therefore, the ratio of the areas A2/A1 is 1.25×10^2.