volume of figures with 2 bases lesson 8.3a standards: m.3.g.2 apply, using appropriate units,...

Volume of Figures With 2 Bases

Lesson 8.3AStandards: M.3.G.2 Apply, using appropriate units, appropriate formulas (area, perimeter, surface area, volume) to solve application problems involving polygons, prisms, pyramids, cones, cylinders, spheres as well as composite figures, expressing solutions in both exact and approximate forms

Definition

Volume:

The number of cubic units needed to fill a space

Or…

The amount of space inside of a 3-D figure

Volume is always measured in cubic units

Volume of a Prism

Volume = B h

B = area of the base

h = height of prism

Example 1

Find the volume of the rectangular prism. Round your answer to the nearest tenth.

2 feet

4 feet

7 feet

Another Example

Find the volume of the triangular prism. Round your answer to the nearest tenth.

18 cm

24 cm

7 cm

Now You Try…

Find the volume of the regular triangular prism. Round your answer to the nearest tenth.

7 inches

15 inches

Volume of a Cylinder

Volume = π r2 h

r = radius of the base

h = height of the cylinder

Example

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

6 cm

18 cm

Now You Try…

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

8 cm

20cm

Word Problems – Example 1

To resurface the football field, the field was dug out 6 inches deep. If dirt costs $15 per cubic yard, how much will it cost to fill the field? A football field is 65 yards wide and 120 yards long.

Word Problems – Example 1 To resurface the football field, the field was dug out 6 inches deep. If dirt costs

$15 per cubic yard, how much will it cost to fill the field? A football field is 65 yards wide and 120 yards long.

1. What kind of mathematical measurement do we need to find?

Volume

2. Once we find volume what should we do?

Multiply it by the cost of dirt.

3. Draw a diagram of the field to help you visualize your problem.

Example 1 Continued

Example 2

Malcom is ordering food and refreshments for a wedding reception for 250 guests. The caterer recommends a sheet cake in the shape of a rectangular prism measuring 24” x 36” x 2”. The cake is cut into 2” x 3” x 2” pieces. How many pieces can be cut from the rectangular cake?

Example 2Malcom is ordering food and refreshments for a wedding reception for 250

guests. The caterer recommends a sheet cake in the shape of a rectangular prism measuring 24” x 36” x 2”. The cake is cut into 2” x 3” x 2” pieces. How many pieces can be cut from the rectangular cake?

Now You Try…

One of the West Delaware water supply tunnels is a 554,400 foot long cylinder with a diameter of 13.5 feet. To the nearest cubic foot, how much earth was removed when the tunnel was built?