MAFS.912.G-GMD.2.4 Practice

MAFS.912.G-GMD.2.4 Practice

3D figures, cross sections, and rotations

Rotating a rectangle about an axis

• the axis acts as a pivot line

• for a vertical rotation, picture a revolving door: the rectangular door spins around a fixed axis/pole, creating a cylinder

• the cylinder created is twice as wide as the rectangular door

• the radius of the cylinder = width of the door, the height of the cylinder = height of the door

Multiple Choice

The two rectangles are rotated about their axes. What is the radius of the cylinder made by the figure on the RIGHT?

• 10 units

• 5 units

• 20 units

Rotating other 2d shapes about an axis

• a triangle rotated about an axis on its side creates a cone

• a rectangle rotated about an axis on its side creates a cone

• a circle rotated about an axis on its diameter creates a sphere

Fill in the Blanks

What 3D figure would be created by rotating this quarter about its diameter?

Multiple Choice

Which revolution will create a cone?

• Rotating a circle about its diameter

• Rotating a circle about its tangent line

• Rotating a triangle about its side

• Rotating a triangle about its vertex

Multiple Choice

What shape is the cross section of the pyramid cut parallel to the base?

• square

• triangle

• isosceles trapezoid

Multiple Choice

A rectangle whose length and width are 10 and 6, respectively, is shown below. The rectangle is continuously rotated around a straight line to form an object whose volume is 150p.

Which line could the rectangle be rotated around?

• the long side

• the short side

• the vertical line of symmetry

• the horizontal line of symmetry