### All Common Core: High School - Geometry Resources

## Example Questions

### Example Question #1 : Geometric Methods To Solve Design Problems: Ccss.Math.Content.Hsg Mg.A.3

You need to build a diagonal support for the bleachers at the local sports field. The support needs to reach from the ground to the top of the bleacher. How the support should look is highlighted in blue below. The bleacher wall is 10 feet high and perpendicular to the ground. The owner would like the support to only stick out 3 feet from the bleacher at the bottom. What is the length of the support you need to build?

**Possible Answers:**

109 ft

11.32 ft

20 ft

10.44 ft

**Correct answer:**

10.44 ft

It is important to recognize that the bleacher, the ground, and the support form a right triangle with the right angle formed by the intersection of the bleacher wall and the ground. We know the bottom of the support should only be 3ft from the bleacher wall on the ground and the bleacher wall is 10ft high. We will use the Pythagorean Theorem to solve for the length of the support, which is the hypotenuse of this right triangle. Our base of the triangle is 3 feet and the leg is 10 feet.

And so we need a support of 10.44 feet long.

### Example Question #1 : Geometric Methods To Solve Design Problems: Ccss.Math.Content.Hsg Mg.A.3

You would like to fill a hollow globe with candy for your students. Since the globe opens upwards at the center, you can only fill the globe halfway. We cannot overfill the globe. If the globe has a radius of 15cm and each spherical candy takes up 2cm^{3} of space, how many candies do you need to fill the globe halfway?

**Possible Answers:**

3,532 candies

14,130 candies

7,065 candies

471 candies

**Correct answer:**

3,532 candies

This is a volume question, asking for the volume of a sphere. There is a twist; we only want half of the volume of the globe. We will start by using the volume formula for a sphere, .

But we want half of the total volume

So we know the volume of half of the globe is 7,065cm^{3}. Since each candy is 2cm^{3}, we divide the volume of the space we need to take up by this amount to find the number of individual candies we need.

We cannot have half of a candy, however, and we do not want to overfill the globe. So we round down to fill the globe with 3,532 candies.