Title: M3.3 Geometry Quiz
Course: Technical Math for Industry > Section: Module 3.3 Volume of Geometric Solids

Q: Find the approximate area of the shaded region below, consisting of a square with a circle cut out of it. Use 3.14 as an approximation for .
- 86 square feet (Correct. The diameter of the circle equals the side length of the square. So the area of the square is square feet. Use the radius of the circle, , to find the area of the circle: square feet The area of the shaded region equals the area of the square minus the area of the circle. This is approximately square feet.)
- 214 square feet (Incorrect. After finding and using this to find the area of the circle, you probably used this number as the side length to find the area of the square. Then you subtracted in the wrong order. The side length of the square is 20. Find the area of the square and then subtract the area of the circle from this.)
- 314 square feet (Incorrect. You found the area of the circle. You need to subtract this from the area of the square to find the area of the shaded region.)
- 856 square feet (Incorrect. You probably found the area of the circle using 20 as the radius instead of 10, and then subtracted the area of the square. Find the approximate area of the circle with and then subtract this from the area of the square.)
A: 86 square feet

Q: Which is the best approximation of the volume of a cylinder with a radius of 10 mm, and a height of 5 mm? Use 3.14 for .
- 785 cubic millimeters (Incorrect. You may have used the correct formula for the volume of a cylinder, , but switched the values for the radius and the height. In this problem, and .)
- 1,570 cubic millimeters (Correct. The volume of a cylinder is . Substitute and into the formula: cubic millimeters)
- 523 cubic millimeters (Incorrect. You used the formula to find the volume, but this is the formula for a cone. Note that is the correct formula for a cylinder.)
- 157 cubic millimeters (Incorrect. You may have forgotten to square the radius in the formula for the volume of a cylinder. Note that is the correct formula for a cylinder.)
A: 1,570 cubic millimeters

Q: The three-dimensional figure below is a solid rectangular prism with a hole in the shape of another rectangular prism going through the center of it. Find the volume of the solid in cubic millimeters.
- 780 (Incorrect. You found the volume of the rectangular prism and the volume of the hole shaped like a rectangular prism, but you added the two volumes instead of subtracting the volume of the hole from the solid.)
- 300 (Correct. First find the volume of the large rectangular prism: Then find the volume of the hole, shaped like a rectangular prism: Subtract the volume of the hole from the volume of the large rectangular prism: The volume of the solid is 300 cubic millimeters.)
- 60 (Incorrect. You may have thought to subtract the larger minus the smaller dimensions and then multiply them together. However, this will not give you the correct volume. You must separately use for the large prism and for the hole. Then subtract the larger volume minus the smaller one.)
- 540 (Incorrect. You found the volume of the rectangular prism, but did not subtract the volume of the hole that is going through the center of it.)
A: 300

Q: Find the length x using the given volume V.
- 3.5 (Correct)
- 4.5 (Incorrect.)
- 6.0 (Incorrect)
A: 3.5

Q: The volume of a cube is cubic centimeters. Find the side length.
A: (a choice with no text)
Feedback: Correct.
Feedback: Incorrect

Q: Find the volume of the doghouse shown.
- or 48.778 (Correct)
- 148.778 (incorrect)
- 4.8778 (incorrect)
A: or 48.778

Q: Find the volume of the pyramid. Round your answer to 2 decimal places.
A: (a choice with no text)
Feedback: Correct
Feedback: Incorrect
Feedback: Incorrect

Q: Find the volume of the right cylinder. Round your answer to 2 decimal places
- 8293.81 or (Correct)
- 8293 (Incorrect)
- 82938.1 (Incorrect)
A: 8293.81 or

Q: Find the volume of the cone. Round your answer to 2 decimal places.
- 29605.39 (Correct)
- 296053.9 (Incorrect)
- 2960.539 (Incorrect)
A: 29605.39