A Rectangular Prism is a 3D solid with rectangular surfaces.

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Presentation transcript:

A Rectangular Prism is a 3D solid with rectangular surfaces. The Volume of a Prism Volume = (Area of the base) × (height) l What is the area of the base? h Abase =lw Volume = lw × h, or w V = lwh

The Surface Area of a Prism Surface Area (SA) = Sum of the Area of each surface l What is the area of the: base & top? top h 4 lateral faces Abase = Atop =lw front & back? A front = Aback =lh w base left & right sides? A left = Aright =wh SA = 2(lw)(lh)(wh)

A Triangular Prism is a 3D solid with triangular surfaces. The Volume of a Prism Volume = (Area of the base) × (height) a What is the area of the base? h Abase = bl (l=ht triangular base) Volume = bl × h, or b V = blh

The Surface Area of a Prism Surface Area (SA) = Sum of the Area of each surface a c top What is the area of the: base & top? h 3 lateral faces Abase = Atop = bl front OR back? A front = hb b base left & right sides? Aright =ah A left =ch SA = (bl)(hb)(ah)(ch)

A Cylinder is a 3D solid. The Volume of a Cylinder A = pr2 V = pr2h r Volume = (Area of the base) × (height) What shape is the base? What is the area of a circle? Therefore, Volume = pr2 × h, or A = pr2 V = pr2h

The Surface Area of a Cylinder C circumference h r C= 2πr SA=2(area of base)+area of curved surface SA=2πr2 + 2πrh

1: Determine the volume of the cylinder Volume = (Area of the base) × (height) 3 cm Volume = (Area of a circle) × (height) Volume = (p × radius2) × (height) 5 cm V = (3.14)(3)2 ×(5) V = (3.14)(9)(5) V = 141.3 cm3

2: Determine the volume of the cylinder Volume = (Area of the base) × (height) Volume = (Area of a circle) × (height) 7 cm Volume = (p × radius2) × (height) What are radius and height measures? 9.2 cm r = 3.5, h = 9.2 cm V = (3.14)(3.5)2(9.2) V = (3.14)(12.25)(9.2) V = 353.9 cm3

3: Determine the height of the cylinder if V = 600 cm3 and r = 5 cm Volume = (Area of the base) × (height) h cm 5 cm Volume = (Area of a circle) × (height) Volume = (p× radius2) × (height) Substitute known values into the formula. 600 = (3.14)(52)h 600 = (3.14)(25)h 600 = (78.5)h 600 78.5 h = 7.6 cm = h

What is the volume of the cylinder? 4. A piece of cardboard measures 20 cm by 8 cm is rolled into a cylindrical shape 20 cm 8 cm r Problem: What is the volume of the cylinder?

Volume = (Area of a circle) × (height) Volume = (p × radius2) × (height) What will we need to determine before we can find the volume? We need to determine the radius. What information will help us determine the radius? The 20 cm measurement will help. How will it help? 20 cm is the circumference of the circle. 20 cm 8 cm r

Circumference = 2p × radius 20 cm 8 cm r Circumference = 2p × radius 2pr = 20 Volume = (Area of a circle) × (height) 2(3.14)r = 20 V = (p × radius2) × (height) 6.28r = 20 20 6.28 r = V = 3.14(3.18)2(8) V = 3.14(10.11)(8) V = 254 cm3 r = 3.18 cm