A family is building a circular fountain in the backyard. The yard is rectangle and measures 14x by 19x and the fountain is going to be circular with a radius of 6x. Once the fountain is built, what will be the area of the remaining yard?
Please do help I already took the test to this I'm just trying to solve the ones I got wrong to raise my grade.
area of yard = (14x)(19x) = 266x^2
area of circle = π(36x^2)
area of remaining yard = 266x^2 - 36πx^2
= (266-36π)x^2
Thanks so much!
can you tell me how to solve it though like the steps so I can try it please.
To find the area of the remaining yard, we need to subtract the area of the circular fountain from the total area of the yard.
First, let's calculate the total area of the yard. The yard is in the shape of a rectangle, and its dimensions are given as 14x by 19x. To find the area of a rectangle, we multiply its length by its width.
Area of the yard = Length * Width
= 14x * 19x
= 266x^2
Now let's calculate the area of the circular fountain. The fountain is circular with a radius of 6x. The formula to find the area of a circle is given by:
Area of a circle = π * (radius)^2
Using the value of π as approximately 3.14, we can substitute the radius value and calculate the area of the circular fountain.
Area of the fountain = 3.14 * (6x)^2
= 3.14 * 36x^2
= 113.04x^2
Finally, we can find the area of the remaining yard by subtracting the area of the circular fountain from the total area of the yard.
Area of remaining yard = Area of yard - Area of fountain
= 266x^2 - 113.04x^2
= 152.96x^2
Therefore, the area of the remaining yard is 152.96x^2.