Two spheres have a scale factor of 1:3. The smaller sphere has a surface area of 16 square feet. Find the surface area of the larger sphere.

Answer 1

Since the scale factor is 1:3, this means that the larger sphere has 3 times the diameter of the smaller sphere, which means it has 3^2 =9 times the surface area of the smaller sphere.

So, if the surface area of the smaller sphere is 16 square feet, then the surface area of the larger sphere is

9*16 =144 square feet

Therefore, the surface area of the larger sphere is 144 square feet

Answer 2

Hi Emmanuel,

Let's take this step by step:

1. First you need to know the equation for the surface area of a sphere:

SA_(sphere) = 4πr²

2. Then you can set the smaller sphere equal to 16 feet for the surface area and solve for the radius:

16 = 4πr²

4/π=r²

r= 4/π

r= 1.12838 ft

3. The ratio of the smaller sphere to the larger sphere is 1:3, so the larger sphere has a radius 3 times the larger sphere. Let's use x to represent the radius of the larger sphere:

x = 3r

x = 1.12838 x 3 = 3.38514 ft

4. Then you can calculate the surface area of the larger sphere using this new radius:

SA_(larger) = 4πx²

4π(11.45916)² = 144 ft²

And that's your answer for the surface area of the larger sphere: 144 ft²

Try to use this as a model for some of the other questions you asked and maybe attempt some of those on your own next.

I hope this helps!