3.4a : Volume of Prisms and Cylindersp. 607-613

GSE’s

Primary

M(G&M)–10–6 Solves problems involving perimeter, circumference, or area of two dimensional figures (including composite figures) or surface area or volume of three

Secondary

M(G&M)–10–2 Makes and defends conjectures, constructs geometric arguments, uses geometric properties, or uses theorems to solve problems involving angles, lines, polygons, circles, or right triangle ratios (sine, cosine, tangent) within mathematics or across disciplines or contexts (e.g., Pythagorean Theorem, Triangle Inequality Theorem)

G-GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.?

CCSS:

Volume- The amount of space inside of a 3-D object

Ex. Finding how much water fits into a pitcher is finding the volume of the pitcher

Volume of any right Prisms or Cylinder:

BhV

Area of baseHeight between the bases(altitude)

Find the volume

Answer

The bases are trapezoids

BhV

))((2

1

trapezoidof

21 bbh

areaB

)65)(4(2

1

22

(22)(h)

= (22)(7)= 154 ft3

Find the Volume

Answer:

V= Bh

B = Area of the Triangle (base)

))((2

1 hb

))(12(2

1 h 9

1512

.222

x

x

theorempyth

254)9)(12(2

1 cm

hcmV 254 cmcmV 1054 2

3540cmV

Find the Volume of the Cylinder

Find the Volume of the CylinderAnswer:

V= Bh

22

2

78.5or 25

5

basecircular of

mmmm

areaB

))( (78.5V 2 hmm

)25)( (78.5V 2 mmmm35.1962V mm

The surface area of a cylinder is 140 square mm.

The radius of the cylinder is 3 mm.

What is the volume of the cylinder?

The surface area of a cylinder is 140 square mm.

The radius of the cylinder is 3 mm.

What is the volume of the cylinder?

Answer: BhV hV 23

Need the height, go back to SA info

h

areaSA

)32(32140

rectangle of area circles 2 2

mmh

h

4.4

)32(32140 2

3

22

4.124

4.43

mm

mmmmV

If the side of a cube is doubled, what happens to the volume?

Find the volume of the steel I-Beam

Find the volume of Toilet paper left on the roll

Home Depot claims this Shed has over 50 cubic feet of storage area. Is

this a correct statement?

[ 1 ft = 12 in][ 1 sq foot = 144 sq inches][1 cubic ft = 1,728 cubic inches]

Find the Volume

Homework