Volumes of Cylinders and Prisms

Match

Match the solids to their names

Sphere

Cylinder

Triangular pyramid

Cone

Rectangular prism

• Sphere

• Cylinder

• Triangular pyramid

• Cone

• Rectangular prism

Match

Match the terms to their definitions

• Area

• Cross section

• Three dimensional

• Two dimensional

the flat space taken up by a 2D object

2D shape created by slicing a 3D object

having length, width, and height

flat

• the flat space taken up by a 2D object

• 2D shape created by slicing a 3D object

• having length, width, and height

• flat

Multiple Choice

What is a scale factor?

• a number that is added to the dimensions of a shape when it is dilated

• a number that represents how many times bigger or smaller a shape or object is than its original size

• A number multiplied by itself

• A number that divides another number

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Fill in the Blanks

Fill in the Blanks

Open Ended

Both containers have the same area on the bottom (or "base").

Imagine the prism contains water 1 cm deep. The water is poured from the prism into the cylinder. How deep is the water in the cylinder? Explain your reasoning.

Open Ended

Both containers have the same area on the bottom (or "base").

If the water in the prism was 3 cm deep and the water were poured into the empty cylinder, what would the height of the water in the cylinder be?

Open Ended

Both containers have the same area on the bottom (or "base").

1. Imagine a third prism whose base is an octagon with the same area as the base of the cylinder. If the water was poured into the octagonal prism, would it still have the same height? Why?

Fill in the Blanks

Multiple Choice

There are also 17 quarters in this stack. Is the volume the same as or different from the first stack?

• Same, because it's the same number of quarters

• Different, because the stack is tilted

The volumes of cylinders and prisms are controlled by the area of the base (bottom) and the height of the figure. Two solids with different shaped bases can have the same volume, as long as the area of the bases are the same and the heights are the same. The shape doesn't actually matter - just the area!

Similarly, solids that are angled or twisted can still have the same volume as one that goes straight up and down, as long as the areas of the cross-sections are the same at every height.

In general, the shape of the base and any twist or angle to the solid doesn't matter for finding volume. All that matters is the area of the base and cross-sections, and the height.

Add these formulas to your digital notebook

Add this property to your digital notebook

If the cross-sections, parallel to the base, of two solids have the same area at every height, then the solids have the same volume

Multiple Choice

What is the formula for the volume of a cylinder, when we know the radius r?

• $$V=\pi r^2h$$

• $$V=lwh$$

• $$V=Bh$$

Dropdown

The radius of the cylinder is ​

Select answer

and the height is ​

Select answer

Drag and Drop

Fill in the formula with the radius and height:

$$V=\pi r^2h$$

$$V=\pi$$ (​

Placeholder

) $$^2$$ (​

Placeholder

)

Drag these tiles and drop them in the correct blank above

8

15

Multiple Choice

What formula would you use to find the volume of this prism?

• $$V=\pi r^2h$$

• $$V=lwh$$

• $$V=Bh$$

Dropdown

The base area B of the prism is ​

Select answer

and the height h is ​

Select answer

Drag and Drop

Fill in the formula with the base area and height

$$V=Bh$$

$$V=$$

Placeholder

$$\times$$ ​

Placeholder

Drag these tiles and drop them in the correct blank above

50

15