BELL WORK FIND THE SURFACE AREA AND VOLUME

BELL WORK: FIND THE SURFACE AREA AND VOLUME OF THE RECTANGULAR PRISM. SA= 2 lw + 2 lh + 2 wh SA=2(20)(9) + 2(20)(8) + 2(9)(8) V = lwh V = (20)(9)(8) V = 1440 cm³ SA = 360 + 320 + 144 SA= 824 cm²

VOLUME WITH THE FORMULA

VOLUME The volume of a solid is the amount of space inside the solid. Volume is measured in cubic units.

FORMULAS When we calculated the volumes we counted the cubes inside: 4 cm 3 cm 10 cm We found the number of cubes that made up the base. Shortcut: We found the area. A = length x width We then calculated how many layers made up the volume. The number of layers is the HEIGHT of the solid. This gives us a formula for calculating other volumes: Volume= Area of Base x Height V = Bh

3 units h 3 units l w One way to find the volume of this prism is to use the formula V = lwh where V is volume, l is length, w is width, and h is height V = lwh V = (3)(3)(3) V = 27 cubic units This formula works very well for rectangular prisms

3 units h Another way to find the volume of this prism is to use the formula V = Bh 3 units w 3 units l where V is volume, B is the area of the base, and h is the height. V = Bh Area of the Base: B = lw B = (3)(3) V = (9)(3) V = 27 cubic units B = 9 square units This formula works very well for non-rectangular prisms

FORMULAS Volume of Rectangular Solids = lwh l = length w = width h = height Volume of NON-rectangular solids = Bh B = Area of the base h = height

YOU TRY: FIND THE VOLUME AND SURFACE AREA OF THE TRIANGULAR PRISM. SA= 2 B + Ph B = (1/2)(9)(4) = 18 P = 4. 5 + 9 + 7. 2 = 20. 7 V = Bh B = (1/2)(9)(4) = 18 V = (18)(8. 1) V = 145. 8 cm³ SA= 2(18) + 20. 7(8. 1) SA = 36 + 167. 67 SA= 203. 67 cm²

EXAMPLE FIND THE VOLUME OF EACH SOLID. V = Bh Area of base = 43 mm² Area of base = (1/2)(4. 8)(7. 2) V = (43)(15) V = (17. 28)(10) V = 645 mm³ V = 172. 8 m³

EXAMPLE Each locker is shaped like a rectangular prism. Which has more storage space? Explain. School Locker Gym Locker V = lwh V = (12)(10)(60) V = (12)(15)(48) V = 7200 in³ V = 8640 in³ The Gym Locker has more storage space because the volume of the gym locker is greater than the school locker.

EXAMPLE A movie theater designs two bags to hold 96 cubic inches of popcorn. Find the height of each bag. Bag A V = Bh B = (3)(4) = 12 96 = 12 h Bag B h=8 V = Bh Height is 8 inches B = (4)(4) = 16 96 = 16 h h=6 Height is 6 inches

PRACTICE: VOLUME AND SURFACE AREA USING THE FORMULA WORKSHEET