BELL WORK: FIND THE SURFACE AREA AND VOLUME OF THE RECTANGULAR PRISM.

SA= 2lw + 2lh + 2wh

SA=2(20)(9) + 2(20)(8) + 2(9)(8)

SA = 360 + 320 + 144

SA= 824 cm²

V = lwh

V = (20)(9)(8)

V = 1440 cm³

VOLUME WITH THE FORMULA

VOLUME

The volume of a solid is the amount of space inside the solid.

Volume is measured in cubic units.

FORMULASWhen we calculated the volumes we counted the cubes inside:

10cm

3cm

4cm

Shortcut: We found the area. A = length x width

We then calculated how many layers made up the volume. The number of layers is the HEIGHT of the solid.

This gives us a formula for calculating other volumes:Volume= Area of Base x Height

V = Bh

We found the number of cubes that made up the base.

One way to find the volume of this prism is to use the formula

V = lwh

where V is volume, l is length, w is width, and h is height 3units

3units

3units

h

w

l V = lwh

V = (3)(3)(3)

V = 27 cubic units

This formula works very well for rectangular prisms

Another way to find the volume of this prism is to use the formula

V = Bh

where V is volume, B is the area of the base, and h is the height.

3units

3units

3units

h

w

l V = Bh

V = (9)(3)

V = 27 cubic units

Area of the Base:

B = lw

B = (3)(3)

B = 9 square units

This formula works very well for non-rectangular prisms

Volume of NON-rectangular solids = Bh

B = Area of the base

h = height

FORMULASVolume of Rectangular Solids = lwh

l = length

w = width

h = height

YOU TRY: FIND THE VOLUME OF THE TRIANGULAR PRISM.

SA= 2B + Ph

B = (1/2)(9)(4) = 18

P = 4.5 + 9 + 7.2 = 20.7

SA= 2(18) + 20.7(8.1)

SA = 36 + 167.67

SA= 203.67 cm²

V = Bh

B = (1/2)(9)(4) = 18

V = (18)(8.1)

V = 145.8 cm³

EXAMPLEFIND THE VOLUME OF EACH SOLID.

V = Bh

Area of base = 43 mm²

V = (43)(15)

V = 645 mm³

V = Bh

Area of base = (1/2)(4.8)(7.2)

V = (17.28)(10)

V = 172.8 m³

EXAMPLEEach locker is shaped like a rectangular prism.

Which has more storage space? Explain.

School Locker

V = lwh

V = (12)(10)(60)

V = 7200 in³

Gym Locker

V = lwh

V = (12)(15)(48)

V = 8640 in³

The Gym Locker has more storage space because the volume of the gym

locker is greater than the school locker.

EXAMPLE

A movie theater designs two bags to hold 96 cubic inches of popcorn. Find the height of each bag.

Bag A

V = Bh

B = (3)(4) = 12

96 = 12h

h = 8

Height is 8 inches

Bag B

V = Bh

B = (4)(4) = 16

96 = 16h

h = 6

Height is 6 inches

PRACTICE:VOLUME USING THE

FORMULAS WORKSHEET