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: 10cm 3cm 4cm 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 We found the number of cubes that made up the base.
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 3units h w l V = lwh V = (3)(3)(3) V = 27 cubic units This formula works very well for rectangular prisms
Another way to find the volume of this prism is to use the formula V = Bh where V is volume, B is the area of the base, and h is the height. 3units h w l V = Bh V = (9)(3) V = 27 cubic units Area of the Base: B = lw B = (3)(3) B = 9 square units This formula works very well for non-rectangular prisms
Volume of NON-rectangular solids = Bh B = Area of the base h = height FORMULAS Volume of Rectangular Solids = lwh l = length w = width h = height
YOU TRY: FIND THE VOLUME OF THE TRIANGULAR PRISM. SA= 2B + Ph B = (1/2)(9)(4) = 18 P = 4.5 + 9 + 7.2 = 20.7 SA= 2(18) + 20.7(8.1) SA = 36 + 167.67 SA= 203.67 cm² V = Bh B = (1/2)(9)(4) = 18 V = (18)(8.1) V = 145.8 cm³
EXAMPLE FIND THE VOLUME OF EACH SOLID. V = Bh Area of base = 43 mm² V = (43)(15) V = 645 mm³ V = Bh Area of base = (1/2)(4.8)(7.2) V = (17.28)(10) V = 172.8 m³
EXAMPLE Each locker is shaped like a rectangular prism. Which has more storage space? Explain. School Locker V = lwh V = (12)(10)(60) V = 7200 in³ Gym Locker V = lwh V = (12)(15)(48) 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 = 12h h = 8 Height is 8 inches Bag B V = Bh B = (4)(4) = 16 96 = 16h h = 6 Height is 6 inches