Volume, Cavalieri's Principle, Rotations, Cross-Sections

Describe the cross section.

• circle
• oval
• semi-circle
• trapezoid

Tags

CCSS.7.G.A.3

What shape will the horizontal cross-section of a sphere be?

• Dome
• Circle
• Ellipse
• Rectangle

Tags

CCSS.HSG.GMD.B.4

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

Tags

CCSS.HSG.GMD.B.4

Which 2-D shape could be revolved about the vertical line to create the 3-D solid?

• 
• 
• 
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Tags

CCSS.HSG.GMD.B.4

What is the exact volume of the pyramid?

• 48 cm³
• 144 cm³
• 288 cm³
• 96 cm³

Tags

CCSS.HSG.GMD.A.1

CCSS.HSG.GMD.A.3

Determine the approximate height of a cone with volume 124 in³ and radius 7 in.

• 2.4 in
• 7.6 in
• 16.9 in
• 8.1 in

Tags

CCSS.HSG.GMD.A.3

What is the radius of a cylinder with volume 300π cm³ and height 12 cm?

• 12.5 cm
• 5√3 cm
• 25 cm
• 5 cm

Tags

CCSS.HSG.GMD.A.1

CCSS.HSG.GMD.A.3

Determine the exact volume of a sphere with diameter of 12 in.

• 2304π in³
• 288π in³
• 48π in³
• 1296π in³

Tags

CCSS.HSG.GMD.A.1

CCSS.HSG.GMD.A.2

CCSS.HSG.GMD.A.3

a) Cavalieri’s Principle states that any two objects with the same cross sectional areas and heights must have the same volume.

• True

• False - the cross sectional areas are not relevant

• False - only the slant height is relevant

• False - even if they have the same cross sectional areas and heights, they cannot have the same volume.

Tags

CCSS.HSG.GMD.A.2

Based on Cavalieri's Principle, will the two prisms have the same volume?

• No, they will not be same. Although the heights are the same, the cross-sections are different shapes. 

• Yes, the heights of both prisms are the same and they have the same cross-sectional area. Therefore, they will have the same volume.
  

Tags

CCSS.HSG.GMD.A.1

CCSS.HSG.GMD.A.2

CCSS.HSG.GMD.A.3