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Geometry 101

Geometry 101. By Breena Darcy. Questions. 1-6. # 1 Which drawing represents the figure?. Assuming the dashed lines represent places where the sheet should be folded, this net should form something close to a triangular based pyramid. Drawing F shows what the final shape should look like.

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Geometry 101

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  1. Geometry 101 By Breena Darcy

  2. Questions 1-6

  3. #1 Which drawing represents the figure? • Assuming the dashed lines represent places where the sheet should be folded, this net should form something close to a triangular based pyramid. Drawing F shows what the final shape should look like.

  4. #2 Which white triangle shows where the black triangle would be if reflected across the x-axis? • Imagine that a mirror is held upright along the x-axis. The reflection of a shape on one side of the mirror would appear to be on the other side of the mirror. The shape's x coordinate would be unchanged, but its y coordinate would be reversed. For example, the reflection of a point located at the coordinate (-3, 2) would appear to have coordinates of (-3, -2).

  5. #3 Which is the closest to the volume of the cone shown above? The volume of a cone is given by this formula: Volume = (1/3) × π × r2 × h where π = a number approximately equal to 3.14 r = the radius of the cone's base h = the height of the cone This cone has a radius of 6 centimeters and a height of 14 centimeters. This cone's volume is about: Volume = (1/3) × π × r2 × h Volume = (1/3) × 3.14 × (6 cm)2 × 14 cm Volume = (1/3) × 3.14 × 36 cm2 × 14 cm Volume = (1/3) × 3.14 × 504 cm3 Volume = (1/3) × 1,582.56 cm3 Volume = 527.52 cm3 Choice H, 527.5 cm2, is the closest to the estimated volume.

  6. #4 Which pair is complementary? • Two angles are complementary if their measures add to 90 degrees. Since is perpendicular to , ∠AFC is a right angle and measures 90 degrees • Since ∠AFB covers one part of ∠AFC and ∠BFC covers the other part, angles AFB and BFC are complementary since, together, they span 90 degrees

  7. #5What is the total area of the figure shown? The area of a triangle is given by this formula: Area of a Triangle = (1/2) × base × altitude From the diagram, we can see that this triangle has an altitude of 12 feet and a base of 14 feet (5 feet + 9 feet = 14 feet). Substituting these values into our formula gives us: Area of a Triangle = (1/2) × base × altitude Area of a Triangle = (1/2) × (14 ft) × (12 ft) Area of a Triangle = (7 ft) × (12 ft) Area of a Triangle = 84 ft2 The total area of the figure is equal to 84 ft2.

  8. #6 An aquarium tank is 3 feet long, 1 foot wide, and 2 feet high. How many gallons of water would it take to fill the tank two-thirds full? (A cubic foot is about 7.5 gallons) First, we need to calculate the volume of the aquarium: Volume of Aquarium = Length × Width × Height Volume of Aquarium = (3 ft) × (1 ft) × (2 ft) Volume of Aquarium = (3 ft) × 2 ft2 Volume of Aquarium = 6 ft3 The aquarium will only be two-thirds full. That volume is: Volume of Water = (2/3)(Volume of Aquarium) Volume of Water = (2/3)(6 ft3) Volume of Water = 4 ft3 Since the problem tells us that a cubic foot of water is about 7.5 gallons, we can calculate the number of gallons in 4 cubic feel: Gallons of Water = (Volume of Water)(7.5 gal/ft3) Gallons of Water = (4 ft3)(7.5 gal/ft3) 30 gal 30 gallons of water will fill an aquarium measuring 3 feet long, 1 foot wide, and 2 feet high two-thirds full.

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