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Warm up

Warm up. Look at this rectangular prism Admire the prism Love the prism Tell the prism it is beautiful Figure out the volume of this prism Figure out the surface area of this prism 7. Tell the prism that it’s shape doesn’t matter, you still love it. 8. 3.5. 6. Prisms.

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Warm up

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  1. Warm up Look at this rectangular prism Admire the prism Love the prism Tell the prism it is beautiful Figure out the volume of this prism Figure out the surface area of this prism 7. Tell the prism that it’s shape doesn’t matter, you still love it 8 3.5 6

  2. Prisms As a Friendly reminder…. Prism- a polyhedron that consists of a polygonal region and its translated image on a parallel plane, with quadrilateral faces! Polyhedron- a geometric solid with solids as faces!!

  3. Friendly reminder continued… Base- the faces that are formed by the polygonal region and its image Lateral faces- the remaining faces which are quadrilaterals Base area- the area of the base Activity 1 identify the bases Label the lateral faces

  4. Note cards (7.2.1) Surface area of a right prism: the surface area, S, of a right prism with lateral area, L, base area B, perimeter p, and height h is given by: S=L+2B or S=hp+2B (7.2.3) Volume of a prism: The volume, V, of a prism with height (h) and base area (B) is given by: V=Bh

  5. Example 1 The net for a right triangular prism is below. What is the prism’s surface area? 2 10 21 17

  6. Answer • The area of each triangular base is A=1/2bh A=½(2x21)=21 • The perimeter of the lateral faces is given by: A=bh A= (10+21+17) x 30= 48 x 30 A=1440 • Thus the surface area is S = 2 (21) + 1440 S = 1482 2 30 10 21 17

  7. Example 2 An aquarium in the shape of an right rectangular prism has dimensions of 110x50x7. Given that 1 gallon = 0.134 cubic feet, how many gallons of water will the aquarium hold? Given 1 gallon = 8.33 pounds, how much will the water weigh? 50 7 110

  8. Answer • The volume of the aquarium is found by using the volume formula: V = lwh V=(110)(50)(7) V=38,500 cubic feet • To approximate the volume in gallons, divide by 0.134: V = 38,500/0.134 287,313 gallons The aquarium will hold 287,313 galllons • To approximate the weight, multiply by 8.33: weight (287,313)(8.33) 2,393,317 pounds The water will weigh 2,393,317 pounds

  9. Activity part 2!! Look at this huge prism that one of your teachers is pointing to. It has a length of 12in A height of 12in And a width of 16in Find the surface area of the net for this rectangular prism Find the volume for this rectangular prism

  10. Answers V=Bh B= 16x12 B=192 H= 12 V= (192)(12) V=2,304 in3 S=2lh+2hw+2lw l=12 w=16 h=12 S= 2(12x12)+(12x16)+(12x16) S=2(144)+2(192)+2(192) S=288+384+384 S=1,056 in2

  11. Example 3 An aquarium has the shape of a right regular hexagonal prism with the dimensions shown at right. Find the volume of the aquarium. 14 7 3 L=14 H=48 W=2(7 3 ) 48

  12. Answer The base of the aquarium has a perimeter of (14) (6) or 84, inches and an apothem of 7 3 inches, so the base area (B) is found as follows: B=1/2ap = 1/2(84)(7 3 ) = 294 3 509.22 square inches. The volume is: V= 1/2ap = 1/2(84)(7 3 )(48) = 14112 3 24,443 cubic inches.

  13. Challenge If you can find the surface area and volume of your juice box, you can drink it. Once you have an answer, raise your hand, and we will confirm if you are right. Then and only then may you drink your juice *do not share your answers! That would be cheating and cheaters never win! (we will be making sure you do not cheat)

  14. Homework

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