The diameter of a sphere is three times that of another sphere.How many times greater is its surface area

surface area of smaller = 4π r^2

surface area of larger = 4π(3r)^2 = 36πr^2
which is 9 times as great

or

the area of similar objects is proportional to the square of their linear dimension,
so 1^2 : 3^2
= 1 : 9

To find out how many times greater the surface area of the larger sphere is compared to the smaller sphere, we need to determine the formula for surface area of a sphere.

The surface area of a sphere is given by the formula:
Surface Area = 4πr^2

Where r is the radius of the sphere.

Since we know that the diameter of the larger sphere is three times that of the smaller sphere, we can establish the relationship between their radii:

Let's say the radius of the smaller sphere is 'r'. Then, the radius of the larger sphere will be '3r' (since the diameter is twice the radius).

Now we can calculate the surface areas of both spheres:

Surface Area of Smaller Sphere = 4πr^2
Surface Area of Larger Sphere = 4π(3r)^2

Simplifying the expression for the larger sphere:
Surface Area of Larger Sphere = 4π(9r^2)
Surface Area of Larger Sphere = 36πr^2

To find out how many times greater the surface area of the larger sphere is compared to the smaller sphere, we divide the surface area of the larger sphere by the surface area of the smaller sphere:

Surface Area Ratio = (Surface Area of Larger Sphere) / (Surface Area of Smaller Sphere)
Surface Area Ratio = (36πr^2) / (4πr^2)

Simplifying the expression:
Surface Area Ratio = 9

Therefore, the surface area of the larger sphere is nine times greater than the surface area of the smaller sphere.