Question

5 ping-pong balls with a total surface area of 320πcm² are placed side by side in a long box. Find the length, in cm of the box. (Answer given in the book is 40cm.) Please help thanks! TT

Answer 1

So the length of the tube will be 5 times the diameter of the balls.

Answer 2

Or in other words, 10 times the radius.

Answer 3

The Surface Area equation involves the radius of the spherical object.
I'll bet we can solve for the radius and then find the length! :)

Answer 4

Here is our equation for surface area.
\[\large A_s=4\pi r^2\]

They told that the TOTAL surface area of the balls is \(320\pi\).
If we divide that value by 5, we'll get the surface area for just 1 ball.

Answer 5

So we can set it up like this.
Here is the surface area of `one ball`.\[\large \frac{320\pi}{5}=4\pi r^2\]From here, we can solve for r to find the radius of `one ball`.

Answer 6

Dividing each side by 4pi gives us,\[\large \frac{320\pi}{20\pi}=r^2\]Which simplifies to,\[\large 16=r^2\]Taking the square root gives us the radius of each ball.
Then we would want to multiply by 2 to get the diameter of each ball.
Then multiply by 5 to get the length of 5 balls (the length of the box).

Answer 7

Thanks so much I understand now! XD