# Expanding brackets and calculating perimeter

• Jan 5th 2010, 06:54 AM
Mukilab
Expanding brackets and calculating perimeter
6)Simplify $\displaystyle (3g)^3$ I couldn't think of an answer for this apart from maybe changing the 3 at the start as because it's 3gx3gx3g so 27g^3?

7)A square has a semicircle cut out of it. Calculate the perimeter of the shape correct to 3dp. (sides of 12cm)
Here I got 54.85 which can't be correct because it says caluclate to 3dp. I did the perimeter as perim=piexdiameter. (then halving this to get semi circle etc etc)
• Jan 5th 2010, 07:06 AM
vonflex1
you can see that also by: $\displaystyle (3*g)^3 = 3^3*g^3$

2) i don't understand: what 3dp means?

if the question is talking about a square with a circle inside that has
a radius of (square's side/2) than you need to add the square's
original perimeter and the circle's perimeter.

that is 48 (square - 12*4) and 12*pi (circle - 2*pi*r)

if i didn't understand the question correctly please clarify...
• Jan 5th 2010, 07:25 AM
Mukilab
Please could you put that into latex? A bit hard to understand that...

What I did was $\displaystyle \text{I added the three sides of the square } 12+12+12=36$ $\displaystyle \text{ then I added that to } \pi \text{ diameter}$

By DP I mean decimal points
• Jan 5th 2010, 07:36 AM
vonflex1
what i meant, again if the question refers to a square with a circle inside,
which radius is half of the square's side...

the perimeter is the original perimeter of the square,

which is 48 (each side 12)

and in addition the inner perimeter of the circle

which is 12*pi (the radius - 6, and the perimeter is 2*pi*radius)

what you still need to to get the decimal representation,

keeping in mind that pi = 3.1415...
• Jan 5th 2010, 07:43 AM
Mukilab
isn't $\displaystyle 2\pi R$ the area? I'll take it as the perimeter, it's all I really needed.
• Jan 5th 2010, 07:51 AM
vonflex1
$\displaystyle 2\pi r$ is the perimeter
$\displaystyle \pi r^2$ is the area
• Jan 5th 2010, 08:32 AM
Soroban
Hello, Mukilab!

Your answer to #7 is correct! . . . (well, sort of).

Quote:

7) A 12-cm square has a semicircle cut out of it.
Calculate the perimeter of the shape correct to 3 decimal places.

Code:

              12       *-------------------*       |:::::::::::::::::::|       |:::::::::::::::::::|       |:::::::::::::::::::|   12 |:::::::* * *:::::::| 12       |:::*          *:::|       |:*              *:|       |*                *|       |                  |       *---------*---------*           6        6

We want the perimeter of the shaded region.

A circle has circumference $\displaystyle 2\pi r$
The semicircle has perimeter: .$\displaystyle \tfrac{1}{2}(2\pi)(6) \:=\:6\pi$ cm.

The three sides of the square has perimeter $\displaystyle 36$ cm.

The perimeter of the shaded region is: .$\displaystyle 6\pi + 36 \;=\;54.84966692$ cm.

Correct to 3 decimal places: .$\displaystyle 54.850\text{ cm}$

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

The problem was not clearly stated.

It did not specify that the semicircle was on the edge of the square
. . nor that it was the largest such semicircle.

In fact, there is a classic problem:
. . "Find the largest semicircle that can be inscribed in a square".

The solution looks like this:
Code:

    o ------*-*-*------o     |    *::::::::::*. |     |  *:::::::::::::::*     | *::::::::::::::* |     |::::::::::::::*  |     *::::::::::::*    |     *::::::::::o      |     *::::::::*        |     |::::::*          |     | *::*            |     o--*---------------o

I'll let you work on it . . .

• Jan 5th 2010, 08:34 AM
Mukilab
Thanks on the great answer and new problem ^^