Solve the word problem. Round your final result to the nearest hundredth.A pattern for Miata’s new carpet design contains circles, semicircles, and quarter-circles. All circular shapes have a radius of 8 cm. What is the area of a pattern that contains 1 circle, 4 semicircles, and 8 quarter-circles? There should be four answers
Area of circle: _____
Area of semicircles: _____
Area of quarter-circles: _____
Total area of pattern: _____
Area of semicircles
Area of semicircles =
Area of circle =
Area of quarter-circles =
Total area of pattern
Area of quarter-circles
Area of circle
Total area of pattern
Answers
Final answer:
The area of the pattern is calculated by finding the area of the circle, semicircles, and quarter-circles separately and then adding them together. The area of the pattern is approximately 1005.31 cm^2.
Explanation:
To find the area of the pattern, we need to calculate the area of the circle, semicircles, and quarter-circles separately. The area of a circle is found using the formula A = πr^2, where r is the radius. So, the area of the circle is A = π(8)^2 = 64π cm^2. The area of a semicircle is half the area of a circle, so it is 32π cm^2. The area of a quarter-circle is a quarter of the area of a circle, which is 16π cm^2. To find the total area of the pattern, we add the areas of the circle, semicircles, and quarter-circles: 64π + 4(32π) + 8(16π) = 64π + 128π + 128π = 320π cm^2. Rounding to the nearest hundredth, the total area of the pattern is approximately 1005.31 cm^2.
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Finding the areas of the circles, semicircles, and quarter-circles separately and combining them together yields the pattern's overall area. The pattern's estimated area is 1005.31 cm^2.
To determine the area of the pattern, individual areas of the circle, semicircles, and quarter-circles are computed separately.
Utilizing the formula
A = πr^2
for a circle with a radius (r) of 8 cm, the circle's area is 64π cm^2.
The semicircles, constituting half the circle's area, total 32π cm^2 each.
Quarter-circles, representing a quarter of the circle's area, contribute 16π cm^2 each.
Combining these, the pattern's total area is calculated as 64π + 4(32π) + 8(16π) = 320π cm^2.
Rounded to the nearest hundredth, the total area is approximately 1005.31 cm^2.
This comprehensive approach ensures the accurate summation of all constituent shapes within the intricate pattern.
Related Questions
What is 8.83 rounded to?
What is the answer to x/5+6=36
List the first 5 multiples.4:7:9:12:
You go shopping an buy x shirts for $12 and y jeans for $28. The Total You spent is $84. a.Write an equation in standard form that models how much money you spent. b. Graph the equation and interpret the intercepts
Answers
there are 4 solutions so we take 4th root to 10^4 which = 10
so 10^4 = 10 * 10 *10 *10
in second example it says 8/27 = ---- * ----- * -----
there are 3 solutions so we take 3th root to 8/27 which = 2/3
so 8/27 = 2*3 * 2/3 * 2/3
the third example it says 64 = --- *---- *------
3 solutions so we take 3th root to 64 which is = 4
so 64 = 4 * 4 * 4
Select each correct answer.
5
6
7
8
Answers
5w - 10 > 20 add 10 to both sides
5w > 30 divide both sides by 5
w > 6
Answer: 7 and 8.
Answer: 7 and 8
Step-by-step explanation:
y=\frac{1}{4}x-3y = 1 4 x − 3
Group of answer choices
please help me!
A) (5,0.5)
B) (8,-1)
C) (-1,8)
D) (0.5,5)
What is the solution to the system of equations?
y=2x-3.5y = 2 x − 3.5
x-2y=-14x − 2 y = − 14
Group of answer choices
(10.5, 7)
(-7, 3.5)
(7, 10.5)
(3.5, -7)
Answers
Answer:
- (x, y) = (8, -1)
- (x, y) = (7, 10.5)
Step-by-step explanation:
1. You can use the expression for y to substitute into the first equation:
2x +4(1/4x -3) = 12
2x +x -12 = 12 . . . . . . eliminate parentheses
3x = 24 . . . . . . . . . . . add 12; next divide by 3
x = 8 . . . . . matches choice C
__
2. You can use the expression for y to substitute into the second equation:
x -2(2x -3.5) = -14
-3x +7 = -14 . . . . . . eliminate parentheses
21 = 3x . . . . . . . . . . add 3x+14; next divide by 3
7 = x . . . . . matches the third choice
_____
When the answer choices are sufficiently different, you only need to find one value to determine which is the correct choice. (If you want to check your work further, you can substitute the other answer value into the two equations to see if it works.)
Answers
question 28:
-2/5 = -0.40
question 29:
20 1/3 = approx 20.333 (the 3 repeats forever)
Answers
Answers
For each of these . . .
The 2nd choice can be any one of the remaining 7.
Total number of ways to pick 2 out of 8 = (8 x 7) = 56 ways .
BUT ...
That doesn't mean you can get 56 different sets of 2 side dishes.
For each different pair, there are 2 ways to choose them . . .
(first A then B), and (first B then A). Either way, you wind up with (A and B).
So yes, there are 56 different 'WAYS' to choose 2 out of 8.
But there are only 28 different possible results, and 2 'ways'
to get each result.