4

A B 7 C

How Much Does It Hold? Pg. 12 Volume of Prisms and Cylinders 8.4 How Much Does It Hold? Pg. 12 Volume of Prisms and Cylinders

8.4 – How Much Does It Hold?___________ Volume of Prisms and Cylinders Today you are going to explore a different measurement found with three-dimensional shapes, called volume.

8.16 – VOLUME Using blocks provided by your teacher, work with your team to build the three-dimensional solid at right. Assume that blocks cannot hover in mid-air. That is, if a block is on the second level, assume that it has a block below it to prop it up.

Yes, there could be a hidden one in the back left a. Is there more than one arrangement of blocks that could look like the solid drawn at right? Why or why not? Yes, there could be a hidden one in the back left

b. To avoid confusion, a mat plan can be used to show how the blocks are arranged in the solid. The number in each square represents the number of the blocks stacked in that location if you are looking from above. For example, in the lower right-hand corner, the solid is only 1 block tall, so there is a "1" in the corresponding corner of its mat plan.

Verify that the solid your team built matches the solid represented in the mat plan above.

c. What is the volume of the solid c. What is the volume of the solid? That is, if each block represents a "cubic unit," how many blocks (cubic units) make up this solid? 13 un3 13 cubic units

8.17 – VOLUME TO MAT PLANS For each of the solids below, build a mat plan for the solid. Then find the volume. Don't forget units.

0 or 1 2 3 2 1 1 V = 9 u3 or V = 10 u3

3 2 1 1 1 1 V = 9 u3

V = 12 u3 V = 11 u3 8.18 – MAT PLANS TO VOLUME For each of the mat plans below, find the volume of the solid. Don't forget units. V = 12 u3 V = 11 u3

8.19 – PRISMS Paul built a tower by stacking six identical layers of the shape at right, one on top of each other.

a. What is the number of cubes on each layer? 7

b. Make a mat plan of the shape. 6 6 6 6 6 6 6

c. What is the volume of his tower? 6 6 V = 42 u3 6 6 6 6 6

d. Paul's tower is an example of a prism because it is a solid and two of its faces (called bases) are congruent and parallel. A prism also has sides that connect the bases (called lateral faces). For each of the prisms below, find the volume. Be ready to share any shortcuts you have developed. Don't forget any units.

4 5 20 un3

6 4 24 un3

12 5 60 un3

Volume of Prisms: V = BH B = Base Area H = Height of Prism

Volume of Cylinders: V =

A = ½(3)(4) A = 6 cm2 8.21 – SPECIAL PRISMS The prism at right is called a triangular prism because the two congruent bases are triangles. a. Shade in the bases of the prism. Find the area of the base of the prism. A = ½(3)(4) A = 6 cm2

b. Find the volume of the triangular prism. V = BH V = (6)(9) V = 54 cm3

Hexagons are congruent parallel bases 8.22 – HEXAGONAL PRISMS What if the bases are hexagonal, like the one shown at right? a. Why are the bases the hexagons and not the rectangles? Shade in one of the bases. Hexagons are congruent parallel bases

b. Find the area of the hexagonal base b. Find the area of the hexagonal base. Leave answers in square root form.

c. Find the volume of the hexagonal prism c. Find the volume of the hexagonal prism. Leave answers in square root form.

8.23 – CYLINDERS Carter wonders, "What if the bases are circular?" Find the volume. Don't forget units. Leave answers in terms of π.