Volume and Cavalieri's Principle

Volume of Solids

Volume of Spheres

Multiple Choice

Find the volume of the given sphere.

• 1,563.5 cubic in.

• 1,325.5 cubic in.

• 1,129.9 cubic in.

• 1,819.6 cubic in.

Multiple Choice

Find the volume of the given sphere.

• 1,4679.8 cubic km

• 995.6 cubic km

• 1,000.9 cubic km

• 1,150.3 cubic km

Multiple Choice

What is the volume of a sphere with a radius of 4 inches? Use 3.14 for pi.

• 561.5 in³

• 267.9 in³

• 201 in³

• 803.8 in³

Volume of Cones

Multiple Choice

Find the volume of the figure.

• 150.72 cm³

• 75.36 cm³

• 452.16 cm³

• 151 cm³

Multiple Choice

Find the volume of the figure.

• 14.13 in³

• 56.52 in³

• 169.56 in³

Multiple Choice

Find the volume of the cone. Round your answers to the nearest tenth. Use 3.14 for π.

Round to the nearest whole number.

• 320.4 in³

• 314 in³

• 205.5 in³

• 267.4 in³

Multiple Choice

Calculate the volume of the pyramid in the picture.  Round to the nearest whole number if necessary.

• 21 m³
• 64 m³
• 32 m³
• 11 m³

Multiple Choice

Find the volume of the rectangular pyramid.

• 364 cm³

• 1092 cm³

• 546 cm³

• 182 cm³

Volume of a Triangular PYRAMID

Multiple Choice

Find the volume of this pyramid.

• 231 cm³

• 62 cm³

• 693 cm³

Multiple Choice

Find the volume of the figure. Round to the nearest whole number.

• 317 units³
• 635 units³
• 1,904 units³
• 890 units³

Cylinders

Multiple Choice

Find the volume of the cylinder.

• 282.7

• 516.2

• 133

• 214

Multiple Choice

Find the volume of the cylinder. Round to the nearest tenth.

• 124.6 in³

• 88 in³

• 97.5 in³

• 78.9 in³

Multiple Choice

What is the volume of the cylinder? Leave you answer in terms of  $$\pi$$  

• $$1584\pi\ km^3$$  

• $$6336\pi\ km^3$$  
  

• $$1584\ km^2$$  

• $$4973.76\ km^2$$  
  

Multiple Choice

a) Cavalieri’s Principle states that any two objects with equal volume must have the same height.

• True

• False - if two objects have equal volume must have the same BASE, not height

• False - if two objects have equal volume must have the same SLANT HEIGHT, not height

• False - if two objects have the same base and height, they must have the same volume.

Multiple Choice

b) A cylinder and a right rectangular prism with equal heights

• These COULD have the same volume

• These MUST have the same volume

• These MUST NOT have the same volume

• Not enough information

Multiple Choice

c) A cylinder and a cone with the same radius

• These COULD have the same volume

• These MUST have the same volume

• These MUST NOT have the same volume

• Not enough information

Multiple Select

Explain what this image is trying to show

• How to calculate the area of the triangles

• That the two triangles have the same area

• That parallel lines show the angles are congruent, therefore the triangles are congruent by ASA

• How to apply the pythagorean theorem

Multiple Choice

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.
  

Multiple Choice

Calculate the volume of a cube with side lengths of 4 inches.

• 64 in³

• 12 in³

• 16 in³

Multiple Choice

What is the volume of this prism?

• 16 cubic cm

• 36 cubic cm

• 144 cubic cm

Multiple Choice

Calculate the volume:

• 1120 ft ³

• 600 ft ³

• 560 ft ³

• 64 ft ³

Multiple Choice

Find the volume of this triangular prism.

• 1440 cm³

• 60 cm³

• 720 cm³

• 180 cm³

Multiple Choice

What is the volume formula for this shape?

• $$V=\frac{Bh}{3}$$  

• $$V=\pi r^2h$$  

• $$V=\frac{\pi r^2h}{3}$$  

• $$V=\frac{4}{3}\pi r^3$$  

Multiple Choice

What is the volume formula for this shape?

• $$V=Bh$$

• $$V=\pi r^2h$$

• $$V=\frac{1}{3}\pi r^2h$$

• $$V=\frac{4}{3}\pi r^3$$

Multiple Choice

What is the volume formula for this shape?

• $$V=l\cdot w\cdot h$$

• $$V=\pi r^2h$$

• $$V=\frac{\pi r^2h}{3}$$

• $$V=\frac{4}{3}\pi r^3$$

Multiple Choice

What is the volume formula for this shape?

• $$V=\pi r^2h$$

• $$V=\frac{Bh}{3}$$

• $$V=\frac{\pi r^2h}{3}$$

• $$V=\frac{4}{3}\pi r^3$$

Multiple Choice

What is the volume formula for this shape?

• $$V=Bh$$

• $$V=\pi r^2h$$

• $$V=\frac{1}{3}\ l\cdot w\cdot h$$  

• $$V=\frac{4}{3}\pi r^3$$

Multiple Choice

A cone has a volume of 12π, and a radius of 2, what is the height?

• 9

• 12

• 2

• 3

Multiple Choice

A cylinder has a volume of 12π and a height of 12, what is the radius?

• 1

• π

• 12

• 24