Unit 3 Geometric Applications UNIT REVIEW s1
Unit 3 – Geometric Applications – UNIT REVIEW
1. Suppose you have a triangle with side lengths 7, 24, 25. Is it a right triangle?
2. A football field is 360 feet by 45 feet. How long is the walk from one corner diagonally to the opposite corner?
3. Using the illustration below, what is the approximate height of the hot air balloon?
4. Explain the Pythagorean Theorem (include drawings). Use a 3, 4, 5 triangle. Make connections between the drawings and the equation.
5. A spider has taken up residence in a small cardboard box which measures 2 inches by 4 inches by 4 inches. What is the length, in inches,of a straight spider web that will carry the spider from the lower right front corner of the box to the upper left back corner of the box?
6. Suppose you have forgotten the formula for finding the volume of a prism or cylinder. What is the critical idea you need to remember in order to find the volume of prisms or cylinders?
7. A candle maker uses a cylinder mold, which is 18 inches tall and has a radius of 1 inch. What is the volume of the candle mold?
(Use 3.14 for.)
8. Which will carry the most water: two pipes, one with a 3 cm radius and the other with a 4 cm radius, or a pipe with a 5 cm radius? (Assume all heights are the same? Show work. Explain.
9.. Find the volume of the sphere shown below. Round your answer to the nearest tenth.
10. A little kid has an ice cream cone (one scoop). It’s a hot day outside, and the ice cream starts to melt. The radius of the cone and the ice cream (sphere) is 4 cm and the height of the cone is 8 cm.
Will all of the melted ice cream fit inside the cone? If it does fit, how much more ice cream will fit in the cone? If it doesn’t fit, how many cubic centimeters of ice cream does he need to eat in order to make it fit?
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Answer Key:
1. Yes – it is a right triangle
2. 362.8
3.. 1498 feet
4. Answer should include a drawing with squares off each side of a right triangle. The area of the squares off the legs will equal the area of the square off the hypotenuse.
5. 6 in
6.. find the area of the base. Multiply the base area times the height
7. 56.52 cubic in.
8. They will both carry the same amount, no matter the length/height of the pipe, because 42 + 32 = 52
9.153.9 in3
10.
4 points- It doesn’t fit. He needs to eat about 42.7p cubic centimeters for it to fit completely. All work must be shown and justification made.
3 points- It doesn’t fit. Both volumes shown, but the question is not answered completely.
2 points—It doesn’t fit. Both volumes shown, but the work is inaccurate and the question is not answered.
1 point—some work shown, partially correct work, but solution is not correct or incomplete.
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