Geometry 101 By Breena Darcy Questions 1 6

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.

#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).

#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 × r 2 × 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 × r 2 × h Volume = (1/3) × 3. 14 × (6 cm)2 × 14 cm Volume = (1/3) × 3. 14 × 36 cm 2 × 14 cm Volume = (1/3) × 3. 14 × 504 cm 3 Volume = (1/3) × 1, 582. 56 cm 3 Volume = 527. 52 cm 3 Choice H, 527. 5 cm 2, is the closest to the estimated volume.

#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

#5 What 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 ft 2 The total area of the figure is equal to 84 ft 2.

#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 ft 2 Volume of Aquarium = 6 ft 3 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 ft 3) Volume of Water = 4 ft 3 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/ft 3) Gallons of Water = (4 ft 3)(7. 5 gal/ft 3) 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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