Geometry Problems

Geometry has many practical applications in everyday life. Estimating heights of objects, finding distances, and calculating areas and volumes are commonplace. One of the most fundamental theorems in geometry, the Pythagorean Theorem, allows us to make many of these calculations. The Pythagorean Theorem states that the square of ...continues

Creative ways to teach surface area and volume.

You are part of a panel of parents, teachers, and administrators working to revise the geometry curriculum for the local high school. On tonight's agenda, you will be brainstorming creative ways to teach surface area and volume. The teachers are especially interested in methods which will help the students connect geometry to li ...continues

Calculating Volume

6. What is the volume of a regular square pyramid which has a total area of 360 if the square base is 10 on a side. 9. How long is the edge of a cube whose total area is numerically equal to it's volume? 15. A cube has a cylinder inscribed inside of it. That cylinder has a sphere inscribed inside of it. What is the rati ...continues

20 algebra problems about quadratic equations

Solve: 1. (4s + 9)^2 = 36 2. f(x) = x^2 + 18x 3. z^2 + 18z + 64 = 0 5. 7n^2 = 10n - 2 6. 5r^2 + 20r = -18 7. -7x^2 - 5x = 9 8. f(x) = 3x^2 - 5x - 1 Find the vertex: 13. f(x) = (x + 6)^2 - 2 Graph: 12. f(x) = -4(x + 7)^2 + 4 15. f(x) = -x^2 + 2x - 7 Find the x and y intercepts: 16. f(x) = 2x^2 + 6x + 1 S ...continues

Geometry Word Problems

The first problem is an attachment. The second problem as follows: 10. The shortest sides of two similar polygons are 5 and 12. How long is the shortest side of a third similar polygon whose area equals the sum of the areas of the others. 18. The radius of a wheel is 35 inches. How far will the wheel travel in 15 revolu ...continues

Geometry Problems

Please explain in full detail the steps to these problems. Do not do #25 instead explain the following: 18. What is the area of a square if the length of a diagonal is 4 sq. rt. 2? 22. The floor of a room is 120 feet by 96 feet. The ceiling is 9 feet above the floor. Everything is to be painted except the floor. (Don’t worr ...continues

Volumes, Areas, Ratios and Proportions

38. if the circumference of a great circle of the Earth is about 40,000 km. the atmosphere of the Earth has an altitude of about 550 km. Find the volume of the Earth and its atmosphere. 39. A steel gas tank has the shape of a sphere. A radius of the inner surface of the tank is 2 feet long. The tank itself is made of 1/4 ...continues

Similar Triangles

Surveying: Surveyors sometimes use similar triangles to measure inaccessible distances. A surveyor could find distance AB by setting up similar triangles ABC and EDC. Assuming all lengths may be directly measured to set up a proportion and solve for AB. 17. How does the surveyor make ABC similar to EDC? 18. Set up a prop ...continues

Unit Conversions, Spheres and Cones

#1 in attachment the solid is made of gold worth $253.75 per ounce One cubic foot weighs 4 pounds. How much is the value of this gold figure? Be careful of the units of measure #3 in attachment Triangle ABC is an equilateral triangle with side of 12. A cone is formed by revolving that triangle above an altitude The lar ...continues

Height, Volume and Diameter

Two similar cones have surface areas of 225 cm^2 and 441 cm^2. 32. If the height of the larger cone is 12 cm, find the height of the smaller cone. 33. If the volume of the smaller cone is 250 cm^3, find the volume of the larger cone. 34. A leg bone of a horse has a cross-sectional area of 19.6 cm^2. What is the diameter of th ...continues