Need help, not sure what I am suppose to do.
Estimate the area between the graph of 4y = 16 - x^2 and the x-axis.
The picture of a mound is on a piece of graph paper. Points A(-4,0) B(0,4)(4,0)
Point B is the top of mound.
To estimate the area between the graph and the x-axis, we can break down the region into smaller shapes and approximate their areas. Since the graph represents a mound, we can divide it into three parts: the triangle AB, the semi-circle BC, and the triangle AC.
To estimate the area of the triangle AB, we can use the formula for the area of a triangle, which is given by:
Area = (1/2) * base * height
In this case, the base is the distance between points A and B, which is 4 units, and the height is the y-coordinate of point B, which is also 4 units. Therefore, the area of triangle AB is:
Area_AB = (1/2) * 4 * 4 = 8 square units.
To estimate the area of the semi-circle BC, we can use the formula for the area of a circle, which is given by:
Area = π * radius^2
In this case, the radius is the distance between points B and C, which is also 4 units. Therefore, the area of semi-circle BC is:
Area_BC = (π/2) * 4^2 = 8π square units.
To estimate the area of the triangle AC, we can use the same formula as triangle AB. The base is the distance between points A and C, which is 8 units, and the height is the y-coordinate of point A, which is 0. Therefore, the area of triangle AC is:
Area_AC = (1/2) * 8 * 0 = 0 square units.
To estimate the total area between the graph and the x-axis, we can sum up the areas of the three shapes:
Total Area = Area_AB + Area_BC + Area_AC
= 8 + 8π + 0
= 8 + 8π square units.
Therefore, the estimated area between the graph of 4y = 16 - x^2 and the x-axis is 8 + 8π square units.