Geometry Math

A vertical slice through a 3-dimensional solid produces a 2-dimensional shape.

Which one of the following solids can produce this 2-dimensional shape when sliced vertically?

• 
• 
• 
• 

Tags

CCSS.7.G.A.3

What is the one shape of cross-section we could create by slicing a right cylinder perpendicular to its base?

• Rectangle

• Ellipse

• Shape with two edges, one straight and one curved

• Circle

Tags

CCSS.7.G.A.3

What solid 3D object is produced by rotating the triangle about line m?

• A cylinder with radius 3 units

• A cylinder with radius 5 units

• A cone with radius 3 units

• A cone with radius 5 units

Tags

CCSS.7.G.A.3

Marcel tried to use Cavalieri's principle to show that the two figures have the same volume:

"The base areas are the same. Therefore, corresponding cross sections have the same area. So the volumes must be the same"

What is the first mistake Marcel made?

• The base areas are not the same

• It isn't true that corresponding cross-sections have the same area.

• He did not establish that the heights are the same

The figures all have the same height and same base area.

For which of the figures can we apply Cavalieri's principle to show they have the same volume?

• Only A and B

• Only A and C

• Only B and C

• A, B, and C

The following cylinder has a volume of 55pi cubic units and a height of 5 units. The cone has the same base area and height, and slant height of 6 units.

What is the volume of the cone?

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

What is the volume of the figure?

Tags

CCSS.7.G.B.6

What is the volume of a cylinder with base radius 2 and height 9?

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Jesse is filling spherical balloons. When full, one of these balloons has a diameter of 24 cm. Jesse can fill a balloon at a rate of 820 cubic cm per breath.

How many breaths does it take Jesse to fill a balloon?

(Nearest whole breath)

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

What is the arc measure of minor arc AB on circle P in degrees?

Tags

CCSS.HSG.C.A.2