Question
The shaded region of the circle has a diameter of 43m and a height of 1.5m
14. Find the area of the shaded region. Round your answer to the nearest tenth.
4712.4 m^2
4057 m^2
195.6 m^2
1138 m^2
14. Find the area of the shaded region. Round your answer to the nearest tenth.
4712.4 m^2
4057 m^2
195.6 m^2
1138 m^2
Answers
GPT 3.5
The area of the shaded region can be calculated by subtracting the area of the triangle from the area of the circle.
The area of the circle is A = πr^2, where r is the radius. Since the diameter is 43m, the radius is half of that: r = 43m / 2 = 21.5m.
So, the area of the circle is A = π(21.5)^2 ≈ 1451.1 m^2.
The area of the triangle is given by A = 0.5bh, where b is the base (which is the diameter of the circle) and h is the height of the triangle (1.5m).
So, the area of the triangle is A = 0.5 * 43m * 1.5m = 32.25 m^2.
Subtracting the area of the triangle from the area of the circle gives us the area of the shaded region: 1451.1 m^2 - 32.25 m^2 ≈ 1418.85 m^2.
Rounding to the nearest tenth, the area of the shaded region is 1418.9 m^2.
Therefore, the closest option is 1138 m^2.
The area of the circle is A = πr^2, where r is the radius. Since the diameter is 43m, the radius is half of that: r = 43m / 2 = 21.5m.
So, the area of the circle is A = π(21.5)^2 ≈ 1451.1 m^2.
The area of the triangle is given by A = 0.5bh, where b is the base (which is the diameter of the circle) and h is the height of the triangle (1.5m).
So, the area of the triangle is A = 0.5 * 43m * 1.5m = 32.25 m^2.
Subtracting the area of the triangle from the area of the circle gives us the area of the shaded region: 1451.1 m^2 - 32.25 m^2 ≈ 1418.85 m^2.
Rounding to the nearest tenth, the area of the shaded region is 1418.9 m^2.
Therefore, the closest option is 1138 m^2.