The surface area of a golf ball is 8.92 in ^2. The surface area of a softball is 53.78 in ^2. Find the ratio of the volumes of a golf ball to a softball. Surface Area = 4π r^2 and Volume = 4/3π r^3

I'm not sure if I did this problem right, but I think the answer is 0.067? Could someone please check my answer?

V/v = (R/r)^3

A/a = (R/r)^2
so,
V/v = (A/a)^3/2
= (53.78/8.92)^3/2
= 6.029^3/2 = 14.80

Oops. You wanted v/V = 0.0675

You are correct

To find the ratio of the volumes of a golf ball to a softball, we need to calculate the volumes of both objects using the formula for the volume of a sphere:

Volume = 4/3π r^3

Let's first calculate the radius of the golf ball. We know that the surface area of a sphere is given by the formula:

Surface Area = 4π r^2

Given that the surface area of the golf ball is 8.92 in^2, we can rearrange the formula and solve for r:

8.92 = 4π r^2

Dividing both sides by 4π, we get:

r^2 = 8.92 / (4π)

r^2 ≈ 0.710

Taking the square root of both sides, we find:

r ≈ √(0.710) ≈ 0.843

Now we can calculate the volume of the golf ball using the formula:

Volume = 4/3π r^3

Plugging in the value of r, we have:

Volume of golf ball = (4/3π) (0.843)^3

Calculating this, we find:

Volume of golf ball ≈ 2.185 in^3 (rounded to three decimal places)

Similarly, we can calculate the radius of the softball using its surface area of 53.78 in^2:

r = √(53.78 / (4π))

r ≈ 1.46

Now we can calculate the volume of the softball:

Volume of softball = (4/3π) (1.46)^3

Calculating this, we find:

Volume of softball ≈ 12.371 in^3 (rounded to three decimal places)

Finally, we can find the ratio of the volumes by dividing the volume of the golf ball by the volume of the softball:

Ratio = Volume of golf ball / Volume of softball

Ratio ≈ 2.185 / 12.371

Ratio ≈ 0.177 (rounded to three decimal places)

Therefore, the correct answer is approximately 0.177, not 0.067 as you suggested.