By Henry and Ethan

Lateral Areas, Surface Areas, and Volumes of Prisms and

Cylinders

PrismsCylinders

Prisms

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How to find the Lateral

area of a Prism

Parts of a Prism-Base: 2 parallel, congruent polygons lying on different planes -Lateral Edges: Adjacent lateral faces intersect

in parallel segments -Lateral Faces: the faces of a prism that are not bases-Altitude: A segment joining the 2 base planes and perpendicular to it. (the length of the altitude is the height )

View parts on Prism

Lateral Area =perimeter x heightPerimeter = add all sides of the shape

togetherLateral Area =(X+Y+Z) x A

How to find the Lateral Area of a Prism

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How to find the surface

area of a Prism

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Theorem-The lateral area of a right triangle equals the perimeter of a base times the height (L.A.=ph)

Surface Area =lateral area x 2bases(multiply the base by 2)

How to find the surface area of a Prism

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How to find the volume

of a Prism

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Surface Area= (X+Y+Z) x 2( ½ x A x X)

Volume= area of base x heightArea of base = (½ x hypotenuse x height of the triangle) Volume= (½ x Z x Y) x X

How to find the Volume of a Prism

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Theorem-The volume of a right prism equals the area of a base times the height of the Prism (V=Bh)

Parts of a Cylinder-Cylinder-like a prism except its bases are circles.

-Altitude-the segment joining the centers of the circle

together. -Radius-the center of a base circle.

Cylinders

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How to find the lateral

area of a cylinder

View parts on cylinder

Lateral Area = 2 x π x radius x height

How to find the Lateral Area of a Cylinder

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How to find the surface

area of a Cylinder

Lateral Area =2 x π x X x Y

View example

Theorem-the lateral area of a cylinder equals the circumference of a base times the height of the cylinder

Surface Area = Lateral Area x 2 x bases (area of a circle)

How to find the surface area of a Cylinder

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How to find the

volume of a

Cylinder

Surface Area = (2πX)y+2(πX²)

View example

Volume = π radius² x the height

How to find the volume of a Cylinder

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View example

Volume = πX²Y

Example on how to find the Lateral Area of a Prism

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Step 1-Find the perimeter

2+2+5=9Step 2-Multiply the perimeter by the

height9 x 10=90

Lateral area =90

Example on how to find the Surface Area of a Prism

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Surface Area-Step 1:find the base area and multiply it by 2 2( ½ x 10 x 7)=70

-step 2:find the lateral area 5+5+10=20

-step 3:multiply the product of the first 2 together

20 x 70=1400Surface Area =1400

Example on how to find the Volume of a Prism

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Volume-Step1: Find the area of the base

½ x 5 x 7=17 ½Step2: Area of the Base x

height17 ½ x 13 =227 ½

Volume=227 ½

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How to find the Lateral Area of a Cylinder

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Lateral Area -Step 1:find circumference of the base

2π 17=106.76

-Step 2:multiply the

circumference by the height. 106.76 x 23=2455.48Lateral Area =2455.48

How to find the Surface Area of a Cylinder

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Surface Area - Step 1: find the lateral area

2π8 x 12=602.88 - Step 2:find the area of

the base π8²=631.02

- Step 3: finish the equation

603 + (2 x 631)=Surface Area =1865

How to find the volume of a Cylinder

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Volume- Step 1:find the area of the circle.

π5²=246.49 - Step 2:multiply the area by the height

246 x 6 Volume = 1476

Parts on a Prism

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Parts of a Cylinder

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