What is the volume of the composite figure shown below?
1 answer:
Answer:
2412 mm³
Step-by-step explanation:
In the figure attached, the composite figure is shown.
Dimension of top rectangular prism:
- length of 13 millimeters
- width of 12 millimeters
- height of 12 millimeters
Volume of top rectangular prism: length*width*height = 13*12*12 = 1872 mm³
Dimension of bottom rectangular prism:
- length of 15 millimeters
- width of 12 millimeters
- height of 3 millimeters
Volume of bottom rectangular prism: length*width*height = 15*12*3 = 540 mm³
Volume of the composite figure: 1872 + 540 = 2412 mm³
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Let ABC be first transformed onto A"B"C" by a 90° clockwise rotation.
Notice that B(4, 1) is mapped onto B''(1, -4). So the rule mapping ABC to A"B"C" is (x, y)→(y, -x)
so we are very close to (-y, -x).
The transformation that maps (y, -x) to (-y, -x) is a reflection with respect to the y-axis. Notice that the 2. coordinate is same, but the first coordinates are opposite.
ANSWER:
"<span>a 90 clockwise rotation about the origin and a reflection over the y-axis</span>"
Let ABC be first transformed onto A"B"C" by a 90° clockwise rotation.
Notice that B(4, 1) is mapped onto B''(1, -4). So the rule mapping ABC to A"B"C" is (x, y)→(y, -x)
so we are very close to (-y, -x).
The transformation that maps (y, -x) to (-y, -x) is a reflection with respect to the y-axis. Notice that the 2. coordinate is same, but the first coordinates are opposite.
ANSWER:
"<span>a 90 clockwise rotation about the origin and a reflection over the y-axis</span>"