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The picture in the attached figure
we know that
the area of the shaded region is equal to
(2/3)*[area of the circle - the area of the triangle]
step 1
Find the area of a circle Ac
Ac = π r²
Ac = π (6)²
Ac = 113.10 units²
step 2
find the area of the triangle At
The triangle is an equilateral triangle with angles on each corner equal to 60 degrees. Meanwhile,
the 3 angles at the center is 120 degrees each since a circle is 360 degree.
We know that the radius (line from centerpoint to corner) is equivalent to 6.
Using the cosine law,
we can calculate for the length of one side.
s² = 6^ + 6² – 2 (6) (6) cos 120
s² = 108
s = 10.4 units
Since this is an equilateral triangle, therefore, all sides are equal.
The area for this is:
At = (sqrt3 / 4) * s²
At = 46.77 units²
step 3
the area of the shaded region=(2/3)*[area of the circle - the area of the triangle]
the area of the shaded region=(2/3)*[113.10-46.77]------> 44.22 units²
therefore
the answer is
the area of the shaded region is 44.22 units²
we know that
the area of the shaded region is equal to
(2/3)*[area of the circle - the area of the triangle]
step 1
Find the area of a circle Ac
Ac = π r²
Ac = π (6)²
Ac = 113.10 units²
step 2
find the area of the triangle At
The triangle is an equilateral triangle with angles on each corner equal to 60 degrees. Meanwhile,
the 3 angles at the center is 120 degrees each since a circle is 360 degree.
We know that the radius (line from centerpoint to corner) is equivalent to 6.
Using the cosine law,
we can calculate for the length of one side.
s² = 6^ + 6² – 2 (6) (6) cos 120
s² = 108
s = 10.4 units
Since this is an equilateral triangle, therefore, all sides are equal.
The area for this is:
At = (sqrt3 / 4) * s²
At = 46.77 units²
step 3
the area of the shaded region=(2/3)*[area of the circle - the area of the triangle]
the area of the shaded region=(2/3)*[113.10-46.77]------> 44.22 units²
therefore
the answer is
the area of the shaded region is 44.22 units²
Answer:
(a) The number of different lock combinations is 216,000.
(b) The probability of getting the correct combination in the first try is .
Step-by-step explanation:
The lock has three-cylinder combinations with 60 numbers on each cylinder.
The procedure of the opening lock is to turn to a number on the first cylinder, then to a second number on the second cylinder, and then to a third number on the third cylinder.
The numbers can be repeated.
(a)
There are three cylinder combinations on the lock, each with 60 numbers.
It is provided that repetitions are allowed.
Then each cylinder can take any of the 60 numbers.
So there are 60 options for the first cylinder.
There are 60 options for the second cylinder.
And there are 60 options for the third cylinder.
So the total number of possible combinations is:
Total number of combinations = 60 × 60 × 60 = 216000.
Thus, the number of different lock combinations is 216,000.
(b)
The events of getting a correct combinations of the three-cylinder combination lock implies that all the three cylinder are set at the correct numbers.
Each cylinder has 60 numbers.
This implies that there are 60 possible ways to get a correct number for the first cylinder.
The probability of getting the correct number for the first cylinder is:
P (Number on 1st cylinder is correct) = .
Similarly for the second cylinder the probability of getting the correct number is:
P (Number on 2nd cylinder is correct) = .
And similarly for the third cylinder the probability of getting the correct number is:
P (Number on 3rd cylinder is correct) = .
So the probability of getting the correct combination in the first try is:
P (Correct combination in the 1st try) = .
Thus, the probability of getting the correct combination in the first try is .
Answer:
226.4 m³.
Step-by-step explanation:
The volume of a right cone with a circular base is:
,
where
is the volume of the cone,
is the radius of the cone,
- and
is the height of the cone.
The radius of the circular base is one-half its diameter.
.
.