algebra help, PLEASE ?????

Question

the surface area of a sphere with radius r is 4(pie)r^2.
1)if we make the radius n times larger, how many times larger is the surface area?
2)if we divide the radius by m what happens to the surface area?
Please tell me how you get these answers. they are a review for the final and i cannot find them. thank you very much.

Answer 1

SA_1 = 4π(r_1)²
SA_2 = 4π(r_2)²

1)
If the new radius is n times the old radius, then r_2 = nr_1, and then it is
SA_2 = 4π(nr_1)²
SA_2 = n² 4π(r_1)²
SA_2 = n² SA_1

Therefore, the surface area is n² times larger.

2) If the new radius is the old radius divided by m, then r_2 = r_1/m. Then
SA_2 = 4π(r_1/m)²
SA_2 = 4π(r_1)²/m²
SA_2 = SA_1/m²

Therefore, the surface area is divided by m².

^_^

Answer 2

if we make the radius n times larger, the surface area will be n^2 as large.
Look at the equation. Everything is the same but the radius. The equation has us square the radius. Lets say the original radius was 2. The equation will have us multiply the rest by 2^2 (or 4). If we double the radius, we will now have 4^2 (or 16). Doubling the radius made the answer 4x as big.

When we divide the radius by 2, (just do the example above backward, going from 4 to 2), the surface area will go from 16 to 4 or 1/4 of what it was.

Answer 3

since you are adjusting or changing the radius for each problem, the answers will vary as a square function.

4pie (nr)^2 for example if n = 2 then the area is 4 times larger
if n = 3 then the ares is 9 times larger, etc.

Answer 4

The surface area varies with the square of the radius. Let's look at your example.

For radius r, the surface area is: 4pi r^2
For radius nr, the surface area is: 4pi (nr)^2 = 4pi n^2 r^2

The ratio between the two is:

(4pi n^2 r^2) / (4pi r^2) = n^2

The other one can be worked out similarly.

For radius r, the surface area is: 4pi r^2
For radius r/m, the surface area is: 4pi (r/m)^2 = 4pi r^2/m^2

(4pi r^2/m^2) / (4pi r^2) = 1/m^2

Answer 5

first of all pie is a food. the ratio of the diameter of a circle to its area is called pi

alright, all you have to is start with V=4(pi)(r^2)
then plug r*n into r
V=4(pi)((r*n)^2)
now you have to solve this so that you get V= (n*something) * (4(pi)(r^2))

the n*something is what the original volume is multiplied by

do the same thing with M

Answer 6

You have the equation for the surface area. Now just see what happens if you change r to nr....

2)...same thing... change r to r/m....

Answer 7

1. n^2, from 4*pi*(rn)^2=(4*pi*r^2)*n^2=old_area*n^2

2. divided by m^2 by same method.

Answer 8

A=4pi r^2
A2 = 4pi(nr)^2 = n^2*A

A3 = 4pi(r/n)^2 = (1/n)^2*A