Question

How much does the percent increase in the surface area if it's radius is doubled.

Answer 1

If it is in case of a circle , it increases 4times more . If other then u r unlucky.

HOPE IT WOULD HELP

Answer 2

◦•●◉✿[ ɦεℓℓσ ]✿◉●•◦


Let’s begin by observing two spheres. The first with standard radius, and the second with double the radius:

[math]A_{1}=4\pi r^{2}[/math]

[math]A_{2}=4\pi (2r)^{2}[/math]

Now, if we want to understand how surface area will increase relative to the first, we have to find a way to express the surface area of the second in terms of the first. We can do this by transitivity:

[math]\frac{r^{2}}{A_{1}}=4\pi=\frac{(2r)^{2}}{A_{2}}[/math]

Thus,

[math]\frac{r^{2}}{A_{1}}=\frac{(2r)^{2}}{A_{2}}[/math]

Let’s continue to simplify:

[math]\frac{r^{2}}{A_{1}}=\frac{4r^{2}}{A_{2}}[/math]

[math]r^{2}A_{2}=4r^{2}A_{1}[/math]

[math]A_{2}=4A_{1}[/math]

But there’s one more step: determining the percent change. As we know, we can calculate percent change like so:

[math]Change=\frac{A_{2}-A_{1}}{A_{1}}\cdot 100[/math]

Substitute and simplify:

[math]\frac{4A_{1}-A_{1}}{A_{1}}\cdot 100=300\%[/math]

There we have it. The surface area will quadruple, and as such, the surface area will increase by 300%!

$thanks { \gamma }^{ \gamma }$