U3L1: Rotating and Slicing

A sphere is pictured below. Select the type of cross section formed when the figure is cut by a horizontal plane.

• circle

• triangle

• hexagon

• rectangle

Answer explanation

When a sphere is cut by a horizontal plane, the cross section formed is a circle. This is because all points on the edge of the cut are equidistant from the center of the sphere, resulting in a circular shape.

Tags

CCSS.HSG.GMD.B.4

A solid is cut by a plane that is parallel to its base, forming a two-dimensional cross section in the shape of a rectangle. Which of the following solids could have resulted in that cross section?

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Tags

CCSS.HSG.GMD.B.4

A solid is cut by a plane that is parallel to its base, forming a two-dimensional cross section in the shape of a square. Which of the following solids could have resulted in that cross section?

• triangular pyramid

• rectangular prism

• cube

• right pentagonal prism

Answer explanation

A cube has all sides equal, so a cross section parallel to its base will always be a square. Other solids like the triangular pyramid or right pentagonal prism do not guarantee a square cross section.

Tags

CCSS.HSG.GMD.B.4

Select the type of cross section formed when a right hexagonal prism is cut parallel to its base.

• square

• pentagon

• triangle

• hexagon

Answer explanation

When a right hexagonal prism is cut parallel to its base, the cross section formed is identical to the base, which is a hexagon. Therefore, the correct answer is hexagon.

Tags

CCSS.HSG.GMD.B.4

Select the type of cross section formed when a right pentagonal prism is cut parallel to its base.

• hexagon

• pentagon

• rectangle

• triangle

Answer explanation

When a right pentagonal prism is cut parallel to its base, the cross section formed is identical to the base shape, which is a pentagon. Therefore, the correct answer is pentagon.

Tags

CCSS.HSG.GMD.B.4

Match the two dimensional shaded region below to the solid formed by rotating the region about the bold axis. (Note: figures not necessarily drawn to scale.)

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Tags

CCSS.HSG.GMD.B.4

A solid is cut by a plane that is perpendicular to its base, forming a two-dimensional cross section in the shape of a rectangle. Which of the following solids could have resulted in that cross section?

• right cone

• rectangular pyramid

• right pentagonal prism

• sphere

Answer explanation

A right pentagonal prism has rectangular cross sections when cut perpendicular to its base. In contrast, a right cone and rectangular pyramid produce triangular sections, and a sphere yields circular sections.

Tags

CCSS.HSG.GMD.B.4

Match the solid below to the two-dimensional shaded region that, upon rotation about the bold axis, would produce the solid. (Note: figures not necessarily drawn to scale.)

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Tags

CCSS.HSG.GMD.B.4

Match the solid below to the two dimensional shaded region that, upon rotation about the bold axis, would produce the solid. (Note: figures not necessarily drawn to scale.)

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Tags

CCSS.HSG.GMD.B.4

Select the type of cross section formed when a right cone is cut parallel to its base.

• pentagon

• circle

• hexagon

• triangle

Answer explanation

When a right cone is cut parallel to its base, the cross section formed is a circle. This is because the cut maintains the same shape as the base, which is circular.

Tags

CCSS.HSG.GMD.B.4