A family is having a pool built in their backyard. If their yard is rectangular and measures 7x by 6x and the pool is circular with a radius of 2x how much of the yard will be left over after the pool is built?
A.38x2
B.42x2 – 4x2
C.42x2 – 2x2
D.38x2
I do not understand these....I have 2 problems like this...can you please explain...thank you
why guess, when you can solve it algebraically? Just take a step back and analyze the given information.
The yard has area (7x)(6x) = 42x^2
The pool has area π(2x)^2 = 4πx^2
It appears to be (B) if you include all the proper symbols
If you want me to just guess I would guess A...but I still don't know how to do them...thanks
No - I would guess B....?
Thank you Steve...I understand now.
Well, let's break it down for you, and hopefully, my clownish humor can help you understand.
First, we need to calculate the area of the yard, which is a rectangular shape with dimensions 7x by 6x. So, the area of the yard is 7x multiplied by 6x, which equals... 42x². Ta-da!
Now, let's calculate the area of the pool, which is circular with a radius of 2x. The area of a circle is found by multiplying π (pi) by the square of the radius. So, the area of the pool is π times (2x)², which is π times 4x². Now, we won't work out the exact value of π because that will just make things messy. Let's keep it simple and just leave it as π.
So, after all the calculations, the area of the pool is 4πx².
Now, to find out how much yard is left over after the pool is built, we subtract the area of the pool from the area of the yard, which is 42x² minus 4πx² (or you could say "42x² minus four pi x squared" if you like to add some math pizzazz).
And the answer, my friend, is option C, 42x² – 2x². Because 4πx² can be simplified to 2x² (since we're not working out the exact value of π).
So, after building the pool, the family will have 42x² – 2x² of yard left. Voila!
Sure! Let's break down the problem step by step.
First, let's visualize the scenario. The yard is rectangular and measures 7x by 6x, which means it has a length of 7x and a width of 6x. The pool is circular with a radius of 2x. We need to find out how much of the yard will be left over after the pool is built.
To find the area of the rectangular yard, we multiply its length by its width:
Yard area = length x width = 7x * 6x = 42x^2
Next, let's find the area of the circular pool. The formula for the area of a circle is:
Pool area = πr^2
where r is the radius. In this case, the radius is 2x, so we substitute it into the formula:
Pool area = π(2x)^2 = 4πx^2
Now, we need to subtract the pool area from the yard area to find the remaining area:
Remaining area = Yard area - Pool area = 42x^2 - 4πx^2
At this point, we can see that the answer options given are not in the same format as our current expression. To make a comparison, we need to find a common denominator. Since π is a constant, we can multiply both the numerator and denominator of the pool area expression by π:
Remaining area = 42x^2 - 4πx^2 / 1
Now the expression can be rewritten as:
Remaining area = (42 - 4π)x^2 / 1
So the equation simplifies to:
Remaining area = 38x^2 - 4πx^2
To determine which answer option matches this remaining area expression, we need to compare it to the answer choices you provided:
A. 38x^2 (Not matching - missing the -4πx^2 term)
B. 42x^2 - 4x^2 (Not matching - missing the π in the second term)
C. 42x^2 - 2x^2 (Not matching - missing the -4πx^2 term)
D. 38x^2 (Not matching - missing the -4πx^2 term)
None of the answer options match our expression, so the correct answer is not provided. It seems there might be a mistake in the answer options you provided. The correct answer is 38x^2 - 4πx^2.