Answer:
(C) 50π
Step-by-step explanation:
For this problem, we need to find a way to relate the inner circle, to the square, to the outer circle.
Given that we know the area of a circle is πr^2, and our inner circle has a area of 25π, we can find the radius.
25π = πr^2
25 = r^2
5 = r
Note, that the diameter of the inner circle is parallel to the side of the square, meaning that the diameter of the inner circle is the length of the side of the square.
diameter = 2 * radius
d = 2 * 5 = 10.
Now that we know the value of the side of the square, we can find the length of the diagonal of the square, which is the diameter of the outer circle.
Using the properties of the 45-45-90 right triangle, we can say that the diagonal of the square is the length of the side times sqrt(2).
Outer_Diameter = 10 * sqrt(2)
Now to find the outer area, we need the formula for the area of a circle. Note that the diameter is twice the radius, so we will simply divide by 2.
A = πr^2
A = π * [ ( 10 * sqrt(2) ) / 2 ]^2
A = π * [ 5 * sqrt(2) ] ^2
A = π * 25 * 2
A = 50π
So the area of the outer circle is 50π.
Cheers.
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Answer:
C. 7 : 18.
Step-by-step explanation:
To solve this, we need to convert each of the measurements given to inches:
2 ft 4 in = 28 inches.
2 yard = 6 feet = 72 inches.
Therefore, expressing this as a ratio would give us:
28 : 72
Simplify by reducing by a factor of 4:
7 : 18. This is the ratio in simplest form.
3/4 x 6 = 18/4 = 4 1/2
She eats 4 1/2 bags of carrots in 6 weeks.
The answer to this problem is simple to find the answer we must see the keywords in the sentence on of is how many which can mean addition/multiplication so here the problem is increasing in a rate of 3 3x1=3
3x2=6 3x3=9 and so on 3x7=21 your answer is 21
Answer:

Step-by-step explanation:
To find the number of kilograms of mercury we need to find how to relate density, mass and, volume. For this we shall recall the density formula:

where
is the density,
is the mass and,
is the volume.
We have the density and want to compute the mass so now we want to know the volume of the pool.
The volume of a rectangular pool is given by the fomula:
.
So for our pool
.
.
Our density is in
, so the last thing we need to do before computing the mass is to express the density in
(this is because we want our mass in
and, we have our volume in
).
For the density conversion we have to remember that



so
.
With this we can finally compute mass:



.