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# Lateral Areas, Surface Areas, And Volumes

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### Lateral Areas, Surface Areas, And Volumes

1. 1. By Henry and Ethan Cylinders Prisms
2. 2. 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 View parts the altitude is the height ) on Prism How to find the Lateral Home area of a Prism
3. 3.  Lateral Area =perimeter x height  Perimeter = add all sides of the shape together  Lateral Area =(X+Y+Z) x A View example Theorem-The lateral area of a right triangle equals the perimeter of a base times the height (L.A.=ph) How to find the surface Home area of a Prism
4. 4.  Surface Area =lateral area x 2bases(multiply the base by 2) Surface Area= (X+Y+Z) x 2( ½ x A x X) View example How to find the Home volume of a Prism
5. 5.  Volume= area of base x height  Area of base = (½ x hypotenuse x height of the triangle)  Volume= (½ x Z x Y) x X View example Theorem-The volume of a right prism equals the area of a base times the height of the Prism (V=Bh) Home
6. 6.  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. View parts on cylinder How to find the lateral Home area of a cylinder
7. 7.  Lateral Area = 2 x π x radius x height Lateral Area =2 x π x X x Y View example How to find Theorem-the lateral area of a cylinder equals the surface the circumference of a base times the height of area of a the cylinder Home Cylinder
8. 8.  Surface Area = Lateral Area x 2 x bases (area of a circle) Surface Area = (2πX)y+2(πX²) View example How to find the volume Home of a Cylinder
9. 9.  Volume = π radius² x the height Volume = πX²Y View example Home
10. 10. Step 1-Find the perimeter 2+2+5=9 Step 2-Multiply the perimeter by the height 9 x 10=90 Lateral area =90 Return to other Home slide
11. 11.  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=1400 Surface Area =1400 Return to other Home slide
12. 12. Volume-Step1: Find the area of the base ½ x 5 x 7=17 ½ Step2: Area of the Base x height 17 ½ x 13 =227 ½ Volume=227 ½ Return to other Home slide
13. 13. 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=2455.48 Lateral Area =2455.48 Return to other slide Home
14. 14. 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 Return to other slide Home
15. 15. 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 Return to other slide Home