Easy GRE Volume Questions Practice Questions

Geometry represents approximately 15% of the Quantitative Reasoning section, with three-dimensional figures serving as a frequent source of easy points for prepared test-takers. Understanding how to calculate the space occupied by solids is essential for success on the exam. This guide focuses on Easy GRE Volume Questions Practice Questions to help you build a solid foundation in three-dimensional geometry. By mastering the basic formulas for cubes, rectangular solids, and cylinders, you can approach these problems with confidence and speed.

For more comprehensive study materials, you can explore our GRE Prep hub. If you are looking for additional practice across all math topics, check out our Free GRE Practice Questions Practice Questions with Answers.

Concept Explanation

Volume is the measure of the three-dimensional space occupied by a solid object, calculated by multiplying the area of a base by the height of the figure. In the context of the GRE, most easy-level questions focus on three primary shapes: rectangular solids (including cubes), cylinders, and spheres. The units for volume are always cubic, such as $\text{cm}^3$ or $\text{in}^3$.

To solve these problems, you must memorize the following standard formulas:

• Rectangular Solid: $V = l \times w \times h$ (length $\times$ width $\times$ height).
• Cube: $V = s^3$ (where $s$ is the length of one edge).
• Cylinder: $V = \pi r^2 h$ (area of the circular base $\times$ height).

Often, the GRE will test your ability to manipulate these formulas. For instance, if you are given the volume and two dimensions of a rectangular solid, you may be asked to find the third dimension. These concepts are also frequently integrated into GRE Practice Questions with Explanations Practice Questions that involve real-world scenarios, such as filling a tank or packing boxes. You can use the AI Question Generator to create more variations of these specific problem types.

Solved Examples

1. Example 1: The Basic Cube
   A cube has an edge length of 4 inches. What is the volume of the cube in cubic inches?
   
   1. Identify the formula for the volume of a cube: $V = s^3$.
   2. Substitute the given edge length: $V = 4^3$.
   3. Calculate the result: $4 \times 4 \times 4 = 64$.
   4. The volume is 64 cubic inches.
2. Example 2: Rectangular Solid Dimensions
   A rectangular box has a length of 10 cm, a width of 5 cm, and a height of 2 cm. What is its volume?
   
   1. Identify the formula: $V = l \times w \times h$.
   2. Plug in the values: $V = 10 \times 5 \times 2$.
   3. Multiply the dimensions: $10 \times 5 = 50$; $50 \times 2 = 100$.
   4. The volume is 100 $\text{cm}^3$.
3. Example 3: Finding Height of a Cylinder
   A right circular cylinder has a volume of $72\pi$ and a radius of 6. What is the height of the cylinder?
   
   1. Start with the cylinder volume formula: $V = \pi r^2 h$.
   2. Substitute the known values: $72\pi = \pi (6^2) h$.
   3. Simplify the equation: $72\pi = 36\pi h$.
   4. Divide both sides by $36\pi$: $h = \frac{72\pi}{36\pi} = 2$.
   5. The height is 2.

Practice Questions

1. A rectangular tank is 8 meters long, 3 meters wide, and 2 meters deep. What is the volume of the tank in cubic meters?
2. If the volume of a cube is 125 cubic centimeters, what is the length of one of its edges?
3. A cylinder has a height of 10 and a base diameter of 4. What is its volume in terms of $\pi$?

4. A box has a square base with sides of length 5 and a volume of 150. What is the height of the box?
5. If the radius of a cylinder is doubled while the height remains the same, by what factor does the volume increase?
6. A cube has a surface area of 24 square inches. What is the volume of this cube?
7. Container A is a cube with side 4. Container B is a rectangular solid with dimensions 2, 4, and 8. Which container has a larger volume?
8. A cylinder has a volume of $100\pi$ and a height of 4. What is the radius of the base?
9. How many cubes with an edge of 2 cm can fit inside a rectangular box with dimensions 4 cm by 6 cm by 8 cm?
10. If a rectangular solid has a volume of 48 and its length and width are 4 and 3 respectively, what is the length of its diagonal?

Answers & Explanations

1. Answer: 48. Using $V = l \times w \times h$, we calculate $8 \times 3 \times 2 = 48$.
2. Answer: 5. The volume of a cube is $s^3$. Since $5^3 = 125$, the edge length is 5.
3. Answer: $40\pi$. The radius is half the diameter, so $r = 2$. Volume $V = \pi (2^2)(10) = 40\pi$.
4. Answer: 6. The area of the square base is $5 \times 5 = 25$. Since $V = \text{Base Area} \times h$, then $150 = 25h$, which means $h = 6$.
5. Answer: 4. The formula is $V = \pi r^2 h$. If $r$ becomes $2r$, the new volume is $\pi (2r)^2 h = 4\pi r^2 h$.
6. Answer: 8. Surface area of a cube is $6s^2 = 24$, so $s^2 = 4$ and $s = 2$. Volume is $2^3 = 8$.
7. Answer: Both are equal. Volume of A = $4^3 = 64$. Volume of B = $2 \times 4 \times 8 = 64$.
8. Answer: 5. $100\pi = \pi r^2 (4)$. Dividing by $4\pi$ gives $r^2 = 25$, so $r = 5$.
9. Answer: 24. Volume of small cube = $2^3 = 8$. Volume of box = $4 \times 6 \times 8 = 192$. $192 / 8 = 24$.
10. Answer: $\sqrt{29}$. First, find height: $48 = 4 \times 3 \times h \rightarrow h = 4$. The diagonal of a rectangular solid is $\sqrt{l^2 + w^2 + h^2} = \sqrt{4^2 + 3^2 + 4^2} = \sqrt{16 + 9 + 16} = \sqrt{41}$. (Correction: Question asked for diagonal, calculation shows $\sqrt{41}$).

For more challenging variations, try our AI-Powered GRE Practice Questions Practice Questions with Answers or the Unlimited GRE Practice Questions Practice Questions with Answers.

1. If a cube's side length is tripled, by what factor does the volume increase?

• A3
• B9
• C27
• D81

Frequently Asked Questions

What is the most common volume formula on the GRE?

The most common formula is for a rectangular solid, $V = lwh$, because it is the basis for many word problems involving tanks and boxes. Understanding the relationship between length, width, and height is crucial for these easy-level questions.

Do I need to memorize the volume of a cone or pyramid for the GRE?

While less common than cylinders or cubes, the GRE occasionally tests these; a cone's volume is $\frac{1}{3}\pi r^2 h$ and a pyramid is $\frac{1}{3} \times \text{Base Area} \times h$. Usually, if a very complex shape is used, the formula might be provided, but basic ones are expected to be known.

How do units affect volume calculations on the GRE?

The GRE may provide dimensions in different units, such as feet and inches, requiring you to convert them to a single unit before calculating volume. Always check the question's required output unit to ensure your final answer matches the requested scale.

What is the difference between surface area and volume?

Volume measures the internal space inside a 3D object, while surface area measures the total area of all the exterior faces. On the GRE, volume is expressed in cubic units and surface area is expressed in square units.

Can volume be negative on the GRE?

No, volume is a physical measure of space and must always be a non-negative value. If your calculation results in a negative number, check your algebraic steps or the signs of the dimensions provided.