Solids and Cross Sections

Figures A and B are 3-D objects. The cross-section of figure A that is parallel to it’s base is the same geometric shape as the cross-section of figure B that is perpendicular to figure B’s base. Based on this information, which of these pairs of 3-D shapes could describe figure A and figure B?

• figure A: rectangular prism; figure B: square pyramid

• figure A: rectangular prism; figure B: cylinder

• figure A: cone; figure B: square pyramid

• figure A: cone; figure B: cylinder

• cone

• cylinder

• pyramid

• prism

A rectangle and a horizontal line segment are shown. What is the resulting object when the rectangle is rotated around the horizontal line segment?

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Describe the cross section.

• triangle
• rectangle
• trapezoid
• square

The equilateral triangle shown is rotated about line a. Each side of the triangle measures 20 mm.

What shape is created by the rotation and what is the approximate circumference of the base?

Circumference of a circle: C = 2πr

• a cylinder with a circumference of about 63 mm

• a cylinder with a circumference of about 126 mm

• a cone with a base circumference of about 63 mm

• a cone with a base circumference of about 126 mm

The square shown has a perimeter of 32 units. The square is rotated about line k.

What shape is created by the rotation and what is the approximate circumference of the base?

Circumference of a circle: C = 2πr

• a cone with a base circumference of about 25 units

• a cone with a base circumference of about 50 units

• a cylinder with a circumference of about 25 units

• a cylinder with a circumference of about 50 units

The triangle is rotated around the indicated axis.  What  is the volume of the resulting figure?

• 75π cm³
• 225π cm³
• 135π cm³
• 405π cm³

The right isosceles triangle shown is rotated about line k with the base forming perpendicular to k. The perimeter of the triangle is 58 units.

Which best describes the resulting three-dimensional shape?

• a cone with a base radius of 17 units

• a cone with a base radius of 34 units

• a cylinder with a base radius of 17 units

• a cylinder with a base radius of 34 units

What shape will the vertical cross-section of a cube be?

• Square
• Triangle
• Trapezoid
• Circle

What 3-D solid is formed when this rectangle is rotated about the vertical line?

• Right, rectangular prism

• Right, circular cylinder

• Right, oval cylinder

• Right, square prism