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.