Geometric Applications

​Unit 3: Geometric Applications of Exponents

Multiple Choice

1. Does the figure to the right form a right triangle? Why or why not?

• A. Yes; A right triangle is formed because the length of the smaller sides add up to the largest side.

• B. Yes; A right triangle is formed because the squares of the smaller sides add up to the square of the largest side.

• C. No; A right triangle was not formed because the length of the smaller sides does not add up to the largest side.

• D. No; a right triangle was not formed because squares of the smaller sides do not add to equal the square of the largest side.

Multiple Choice

2. Find the length of the missing side of the right triangle.

• A. $$\sqrt{12.96}$$

• B. $$\sqrt{5.6}$$

• C. $$\sqrt{16.96}$$

• D. $$\sqrt{7.2}$$

Multiple Choice

3. What is the height of the cone if the slant height is 13 cm?

• A. 8 cm

• B. 18 cm

• C. 144 cm

• D. 12 cm

Multiple Choice

4. Find the distance between point A and point B as shown on the coordinate plane below.

• A. 10 units

• B. 14 units

• C. 100 units

• D. 9 units

Multiple Choice

5. Find the volume of the cylinder. Leave your answer in terms of π.

• A. $$70\pi\ cm^3$$

• B. $$17\pi\ cm^3$$

• C. $$1320\pi\ \ cm^3$$

• D. $$490\pi\ cm^3$$

Multiple Choice

6. Find the volume of the cone. Use 3.14 for π.

• A. $$858.3\ cm^3$$

• B. $$769.3\ cm^3$$

• C. $$329.7\ cm^3$$

• D. $$245\ cm^3$$

Multiple Choice

7. If the basketball shown below has a radius of 6 inches from the center to the outside surface, approximately how many cubic inches of air will it hold when fully inflated?

• A. $$904.32\ in^3$$

• B. $$288\ in^3$$

• C. $$1808.64\ in^3$$

• D. $$72\ in^3$$

Multiple Choice

8. Chris is planning to fill up a kiddie swimming pool for his younger sister but he does not have a water hose. He has decided to use a cylindrical bucket with a diameter of 12 inches and a height of 14.5 inches. He has already calculated the approximate volume of the kiddie pool to be able to hold about 60,000 cubic inches of water. Approximately how many buckets of water will he need to use in order to fill the kiddie pool?

• A. Approximately 9 buckets

• B. Approximately 115 Buckets

• C. Approximately 37 buckets

• D. Approximately 29 buckets

Multiple Choice

9. A sphere has been placed inside a cylinder with the same dimensions; both have a radius of 6 cm, and a height of 12 cm. How many cubic centimeters of space does the sphere NOT fill up?

• A. $$432\pi\ cm^3$$

• B. $$72\pi\ cm^3$$

• C. $$288\pi\ cm^3$$

• D. $$144\pi\ cm^3$$