Volume: Prisms and Cylinders (10-7) What is volume? How do you find volume of a prism? Volume: three dimensional area (space inside a solid) measured in cubic units (how many cubes that are 1 __ long on each side it takes to fill up a figure) and expressed as “units cubed” (Examples: in.3, cm.3) Volume of a Prism Formula Volume. (pyramid) = B  h where B is the area of the Base and h is the height Proof: volume (V) = the area of the first “layer” (B) · the number of layers (h) In the rectangular prism to the right, it takes 8 · 5 = 40 cubes to fill up the bottom layer of the prism. Since it takes 4 layers of cubes to fill up the container, it takes 40 · 4 = 160 cubes to fill up the prism

Volume: Prisms and Cylinders (10-7) Example: Find the volume of the following triangular prism. If we make the prism sit on an end, then the base is one of the triangles on the ends. V(prism) = Bh B = ½ · base (b)  height (h) of a triangle B = ½  10  6 = 30 = 30 (21) = 630 The volume of the triangular prism is 630 cm3.

Find the volume of the triangular prism. Volume: Prisms and Cylinders LESSON 10-7 Additional Examples Find the volume of the triangular prism. V = Bh Use the formula for volume. = 63 • 20 B = • 9 • 14 = 63 cm2 1 2 = 1,260 Simplify. The volume is 1,260 cm3.

Volume: Prisms and Cylinders (10-7) How do you find volume of a cylinder? Volume of a Cylinder Formula Volume. (cylinder) = B  h where B is the area of the Base and h is the height [In other words, volume of a cylinder = area of the first layer (base) · the number of layers (height)]. Example: Find the volume of the orange juice can to the nearest cubic centimeter (cm3).   If we make the cylinder sit on an end, then the base is one of the circles on the ends. V = Bh B = r2 = r2h =  (3.4)2(12) r = 3.4, h = 12 =  (11.56)(12) = 138.72  435.5808 The volume of the cylinder is about 436 cm3.

Find the volume of the juice can to the nearest cubic centimeter. Volume: Prisms and Cylinders LESSON 10-7 Additional Examples Find the volume of the juice can to the nearest cubic centimeter. V = Bh Use the formula for volume. V = r 2h B = r 2 (Substitute)   • (3.4)2 • 16 Replace r with 3.4, and h with 16.  3.14 • 11.56 • 16 Use 3.14 for   580.7744 Simplify. The volume is approximately 581 cm3.

Find the volume of each space figure. Volume: Prisms and Cylinders LESSON 10-7 Lesson Quiz Find the volume of each space figure. 1. rectangular prism with base 12 m by 14 m and height 50 m 2. cylindrical pool with diameter 24 ft and height 4 ft 3. right triangular prism with base legs 8 cm and 10 cm and height 20 cm 8,400 m3 about 1,809 ft3 800 cm3