A piece of fabric measures 3.9 meters express this length in centimeters

DochEvi [55]

Answer:

12pi cm

Step-by-step explanation:

The Perimeter of the full shape is the sum of the lengths of the edges of the parts. For convenience in referencing them, we'll call the large curve " $curve_{big}$ " and the three smaller curves " $curve_1$ " " $curve_2$ " " $curve_3$ " in order from left to right.

Thus, the Perimeter of the full shape can be written as an equation:

$P_{overall} = Length(curve_{big})+Length(curve_1)+Length(curve_2)+Length(curve_3)$ Since all of those edge lengths are curves, and the question states that all of the curves are made from parts of circles, then we need to know how to find the length of the edge of a circle.

<u>Parts of a circle</u>

Since values in the diagram are diameters, use the formula for the Perimeter of a circle $P=\pi d$ (where d is the diameter).

Let's call the diameters of each of our curves " $d_{big}$ " " $d_1$ " " $d_2$ " " $d_3$ ", with the subscripts denoting which curve we're referring to.

Note that for each curve, the curve only represents half of a circle. So, to find the length of each curve, we'll need half of the full perimeter of each circle.

So for instance: $Length(curve_{big})=\frac{1}{2} \pi d_{big}$

Substituting back into the main equation above:

$P_{overall} = Length(curve_{big})+Length(curve_1)+Length(curve_2)+Length(curve_3)$ $P_{overall}=\frac{1}{2} \pi d_{big} + \frac{1}{2} \pi d_{1} + \frac{1}{2} \pi d_{2} + \frac{1}{2} \pi d_{3}$

Note that all terms have common factors of "one-half" and "pi" in them. These can be factored out:

$P_{overall}=\frac{1}{2} \pi (d_{big} + d_{1} + d_{2} +d_{3})$

The diameter for the large Curve, is the sum of the three small diameters, so $d_{big}=12cm$ , and $d_{1}=d_{2}=d_{3}=4cm$

Substituting and simplifying (in terms of pi):

$P_{overall}=\frac{1}{2} \pi ( (12cm) + (4cm) + (4cm) + (4cm) )\\P_{overall}=\frac{1}{2} \pi ( 24cm)\\P_{overall}=12 \pi cm$

<u>Additional Understanding</u>

Interesting for this problem, since the diameters of the 3 small curves formed the diameter of the large curve $d_{1} + d_{2} + d_{3} =d_{big}$ , one could make a different substitution into one of our formulas above:

$P_{overall}=\frac{1}{2} \pi (d_{big} + d_{1} + d_{2} +d_{3})$

$P_{overall}=\frac{1}{2} \pi (d_{big} + (d_{big}))$

$P_{overall}=\frac{1}{2} \pi (2d_{big})$

$P_{overall}=\pi d_{big}$

Notice that $\pi d_{big}$ is just the full perimeter of a circle with the big diameter.

So, if one imagined starting with a full circle with the big diameter, even though the bottom half of the circle was turned into a bunch of smaller half circles, since they were in a line along the diameter of the large circle, the full perimeter of the new shape didn't change.

The number of smaller circles doesn't need to be 3 either... as long as it goes the full distance across, right along the diameter.

7 0

2 years ago

A farmer builds a rectangular pen with a perimeter of 116 ft if the rent is 5 feet more than the width what is the width

kondaur [170]

The area is 116, so we can plug that in for A. Now, we cant solve the equation yet because it still has two variables. Since we know the length is 5 feet greater than the width, we can rewrite l in terms of w. So this is how the new equation would look like

116=2(w+5)+2w

Answer:
116=2w+10+2w
106=4w
w=26.5 ft.
The width is 26.5 ft.

3 0

4 years ago

Which statement about this equation is true?

Viktor [21]

The equation has no solution because:

5(n+10)=5n+10n
5n+10n=5n+10n
I subtract 5n from both sides
10n=10n
Only one side is supposed to have the variable which is n, so the equation has no solution.

4 0

3 years ago

If 45 cookies will serve 15 students, how many cookies are needed for 30 students

valina [46]

90 cookies will feed 30 people just double 45

8 0

4 years ago

Read 2 more answers

The basketball court at Cecil College is 50 feet by 94 feet. they need to buy fencing to go around the outside of the court in o

vitfil [10]

So the fencing perimiter is 70 by 114
perimiter=2 times width +2 times legnth
width=70
legnth=144
perimiter=70 times 2+114 times 2=140+228=368
needs to buy 368 feet

7 0

3 years ago