A globe has a diameter of 24 inches. A smaller globe has a diameter of 18 inches. What is the surface area volume ratio of the smaller globe

area = 4 pi r^2

volume = 4/3 pi r^3

So, for any sphere, the area:volume ratio is 3/r

However, I suspect that you garbled the question. Since area varies as the square of the diameter, if the diameters are in the ratio 3/4,

area is in the ratio (3/4)^2
volume is in the ratio (3/4)^3

To calculate the surface area-to-volume ratio of a sphere, we need to find the surface area and volume of the sphere and then divide the surface area by the volume.

First, let's calculate the surface area of the smaller globe. The surface area of a sphere is given by the formula:

Surface Area = 4πr^2

where r is the radius of the sphere. To find the radius of the smaller globe, we divide its diameter by 2:

Radius of smaller globe = 18 inches / 2 = 9 inches

Using this radius value, we can calculate the surface area of the smaller globe:

Surface Area of smaller globe = 4π(9)^2 = 4π(81) = 324π square inches

Next, let's calculate the volume of the smaller globe. The volume of a sphere is given by the formula:

Volume = (4/3)πr^3

Using the radius value we found earlier:

Volume of smaller globe = (4/3)π(9)^3 = (4/3)π(729) = 972π cubic inches

Now, we can calculate the surface area-to-volume ratio by dividing the surface area by the volume:

Surface area-to-volume ratio of smaller globe = Surface Area / Volume
= (324π) / (972π)
= 1/3

Therefore, the surface area-to-volume ratio of the smaller globe is 1/3.