Answer:
31.4 in³
Step-by-step explanation:
The box is just big enough to hold the 3 balls, so it must have a length 6 times the radius of each ball, a width 2 times the radius, and a height 2 times the radius.
The volume of the box is:
V = (6r)(2r)(2r)
V = 24r³
The volume of the 3 balls is:
V = 3 (4/3 π r³)
V = 4πr³
So the volume of the air is:
V = 24r³ − 4πr³
V = (24 − 4π) r³
Since r = 1.4 inches:
V = (24 − 4π) (1.4 in)³
V ≈ 31.4 in³
Given that ABC is a triangle and is reflected over the y - axis, reflected over the x - axis and rotated 180°
We need to determine the coordinates of the point A'
<u>Reflection over the y - axis:</u>
The coordinates of the point A is (-2,1)
The transformation rule to reflect across the y - axis is
Substituting the point (-2,1) in the rule, we get;
Thus, the coordinates of the point A after reflection over the y - axis is (2,1)
<u>Reflection over the x - axis:</u>
The transformation rule to reflect across the x - axis is
Substituting the point (2,1) in the rule, we get;
Thus, the coordinates of the point A after reflection over the x - axis is (2,-1)
<u>Rotation about 180°:</u>
The transformation rule to rotate about 180° is
Substituting the point (2,-1) in the rule, we get;
Thus, the coordinates of the point A after the rotation about 180° is (-2,1)
Therefore, the coordinates of the point A' is (-2,1)
Hence, Option B is the correct answer.