Example Question #1 : Geometry
Calculate the volume of the cone provided. Round the answer to the nearest hundredth.
In order to solve this problem, we need to recall the formula used to calculate the volume of a cone:
Now that we have this formula, we can substitute in the given values and solve:
Example Question #2 : Geometry
Observe the location of the black and orange angles on the provided coordinate plane and identify which of the following transformations—rotation, translation, or reflection—the black angle has undergone in order to reach the position of the orange angle. Select the answer that provides the correct transformation shown in the provided image.
A translation down
A translation to the left
A reflection over the x-axis
First, let's define the possible transformations.
Rotation: A rotation means turning an image, shape, line, etc. around a central point.
Translation: A translation means moving or sliding an image, shape, line, etc. over a plane.
Reflection: A reflection mean flipping an image, shape, line, etc. over a central line.
In the images from the question, notice that the black angle rotates counterclockwise, or left around the y-axis. The vertical, base, line of the angle goes from being the base, to the top; thus the transformation is a rotation.
The transformation can't be a reflection over the x-axis because the orange angle didn't flip over the x-axis.
The transformation can't be a translation because the angle changes direction, which does not happened when you simply move or slide an angle or image.
Example Question #3 : Geometry
What is the scale of the dilation that the blue rectangle underwent to get the purple rectangle in the image provided?
A dilation creates an image of the same shape, but of a different size. Dilations are always done with a certain scale factor. Let's look at the image in the picture and determine the length and width of each of the rectangles:
Notice that both the length and the width of the rectangle doubles in the purple rectangle, from the blue rectangle; thus the scale of the dilation is