Finding area and volume using Cavalieri's principle

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.3

CCSS.8.G.C.9

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.

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.
  

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.3

CCSS.8.G.C.9

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.3

CCSS.8.G.C.9

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

CCSS.8.G.C.9

What is the exact volume of the pyramid?

• 48 cm³
• 144 cm³
• 288 cm³
• 96 cm³

Tags

CCSS.HSG.GMD.A.3

Describe the cross-section.

• square
• rectangle
• triangle
• circle

Tags

CCSS.7.G.A.3

According to Cavalieri's Principle, how many disks could fit inside the cylinder?

• 12 disks

• 6 disks

• 10 disks

Determine whether the 3-D figures are congruent to each other. (Hint: Find the area of the cross-sectional shapes).

• False. Although the cross-sectionals' area and heights of the 3-D figures are the same,the shapes are not congruent

• True. The cross-sectionals' area and the heights of the 3-D figures are the same. They don't have to be the same shape.

• False. The cross-sections are not the same shape.

• True. All the shapes are 3-D figures and the same height.

Tags

CCSS.8.G.A.2