Volume of Prisms - Pre Algebra

1. A prism has a base area of 15 square cm and a height of 8 cm. What is its volume?

   120 cubic centimeters, since $V = Bh = 15 \times 8$.

2. What kind of units does volume use?

   Cubic units, such as cubic centimeters or cubic feet.

3. What is the volume formula for a right rectangular prism?

   $V = lwh$: length times width times height.

4. How many cubes with edge $\frac{1}{2}$ in fill a box that is 2 in by 1 in by 1 in?

   16 cubes. The box is 4 by 2 by 2 half-inch cubes, and $4 \times 2 \times 2 = 16$.

5. A rectangular prism has volume 120 cubic cm and a base 6 cm by 4 cm. What is its height?

   5 cm. The base area is 24, and $120 \div 24 = 5$.

6. A pool is 25 m long, 15 m wide and 2 m deep throughout. What is its volume?

   750 cubic meters, since $25 \times 15 \times 2 = 750$.

7. What is the volume of a box that is 2.5 ft by 4 ft by 3 ft?

   30 cubic feet, since $2.5 \times 4 = 10$ and $10 \times 3 = 30$.

8. What is the general volume formula for any prism?

   $V = Bh$, where $B$ is the area of the base and $h$ is the height.

9. What is the volume of a rectangular prism that is 4 cm by 6 cm by 10 cm?

   240 cubic centimeters, since $4 \times 6 \times 10 = 240$.

10. What is the volume of a cube with edge length 4 in?

    64 cubic inches, since $4^3 = 64$.

11. What is the volume of a slab 20 ft long, 12 ft wide and 1.5 ft deep?

    360 cubic feet, since $20 \times 12 \times 1.5 = 360$.

12. Each dimension of a rectangular prism is doubled. By what factor does its volume change?

    It is multiplied by 8, since $2 \times 2 \times 2 = 8$.

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