PRE-ALGEBRA

PRE-ALGEBRA

What is volume?

How do you find volume of a prism?

Volume of a Prism Formula

Volume. (pyramid) = B h

where B is the area of the Base and h is the height

Volume: Prisms and Cylinders (10-7)

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)

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

Proof: volume (V) = the area of the first “layer” (B) · the number of layers (h)

PRE-ALGEBRA

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.

PRE-ALGEBRA

Find the volume of the triangular prism.

The volume is 1,260 cm3.

V = Bh Use the formula for volume.

= 63 • 20 B = • 9 • 14 = 63 cm212

= 1,260 Simplify.

LESSON 10-7

Additional Examples

Volume: Prisms and Cylinders

PRE-ALGEBRA

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)].

Volume: Prisms and Cylinders (10-7)

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.

PRE-ALGEBRA

Find the volume of the juice can to the nearest cubic centimeter.

The volume is approximately 581 cm3.

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.

580.7744 Simplify.

LESSON 10-7

Additional Examples

Volume: Prisms and Cylinders

3.14 • 11.56 • 16 Use 3.14 for

PRE-ALGEBRA

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

800 cm3

8,400 m3

about 1,809 ft3

LESSON 10-7

Volume: Prisms and Cylinders

Lesson Quiz