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# Geometry Word Problems Practice Questions Set 5

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Updated on Sep 26, 2011

## Geometry Word Problems

The geometry problems in this set  involve lines, angles, triangles, rectangles, squares, and circles. You will learn how to find length, perimeter, area, circumference, and volume, and how you can apply geometry to everyday problems.

1. A sphere has a volume of 288π cm3. Find its radius.
1. 9.5 cm
2. 7 cm
3. 14 cm
4. 6 cm
2. Using the illustration provided below, if mABE = 4x + 5 and m CBD = 7x – 13, find the measure of ABE.
1. 151°
2. 73°
3. 107°
4. 29°
3. Two angles are complementary. The measure of one angle is four times the measure of the other. Find the measure of the larger angle.
1. 36°
2. 72°
3. 144°
4. 18°
4. If Gretta's bicycle has a 25-inch diameter wheel, how far will she travel in two turns of the wheel? (π = 3.14)
1. 491 in
2. 78.5 in
3. 100 in
4. 157 in
5. Two angles are supplementary. The measure of one is 30 more than twice the measure of the other. Find the measure of the larger angle.
1. 130°
2. 20°
3. 50°
4. 70°
6. Using the illustration provided, find the mAED. Given mBEC = 5x – 36 and mAED = 2x + 9.
1. 141°
2. 69°
3. 111°
4. 39°
7. The measures of the angles of a triangle are in the ratio of 3:4:5. Find the measure of the largest angle.
1. 75°
2. 37.5°
3. 45°
4. 60°
8. A mailbox opening is 4.5 inches high and 5 inches wide. What is the widest piece of mail able to fit in the mailbox without bending? Round answer to the nearest tenth.
1. 9.5 inches
2. 2.2 inches
3. 6.7 inches
4. 8.9 inches
9. The figure below represents the cross section of a pipe inch thick that has an inside diameter of 3 inches. Find the area of the shaded region in terms of π.
1. 8.75πin2
2. 3.25πin2
3. 7πin2
4. 1.75πin2
10. Using the same cross section of pipe from question 464, answer the following question. If the pipe is 18 inches long, what is the volume of the shaded region in terms of π?
1. 31.5πin3
2. 126πin3
3. 157.5 in3
4. 58.5 in3
11. A person travels 10 miles due north, 4 miles due west, 5 miles due north, and 12 miles due east. How far is that person from the starting point?
1. 23 miles northeast
2. 13 miles northeast
3. 17 miles northeast
4. 17 miles northwest
12. Using the illustration provided, find the area of the shaded region in terms of π.
1. 264 – 18π
2. 264 – 36π
3. 264 – 12π
4. 18π – 264
13. Find how many square centimeters of paper are needed to create a label on a cylindrical can 45 cm tall with a circular base having diameter of 20 cm. Leave answer in terms of π.
1. 450π cm2
2. 4,500π cm2
3. 900π cm2
4. 9,000π cm2
14. Using the illustration provided below, if the measure AEB = 5x + 40 and BEC = x + 20, find mDEC.
1. 40°
2. 25°
3. 140°
4. 65°
15. The structural support system for a bridge is shown in the illustration provided. is parallel to is parallel to is parallel to . Find CGE.
1. 46°
2. 52°
3. 82°
4. 98°
16. Find the area of the shaded portions, where . Leave answer in terms of π.
1. 25π – 72
2. 25π – 48
3. 25π – 8
4. 100π – 48
17. Find the area of the shaded region in terms of π.
1. 12 – 9π
2. 36 – 9π
3. 36 – 4.5π
4. 2π – 16
18. On a piece of machinery, the centers of two pulleys are 3 feet apart, and the radius of each pulley is 6 inches. How long a belt (in feet) is needed to wrap around both pulleys?
1. (6 + .5π) ft
2. (6 + .25π) ft
3. (6 + 12π) ft
4. (6 + π) ft
19. Find the measure of each angle of a regular 15-sided polygon to the nearest tenth.
1. 24°
2. 12°
3. 128.6°
4. 156°
20. A sand pile is shaped like a cone as illustrated below. How many cubic yards of sand are in the pile. Round to the nearest tenth. (π = 3.14)
1. 5,358.9 yd3
2. 595.4 yd3
3. 198.5 yd3
4. 793.9 yd3

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