Math worksheet for finding volume of cubes and rectangular prisms with corresponding answers.

Here are the step-by-step solutions for each problem on the worksheet.

1) A cube has width of 9 cm. What is the volume of the cube?
* Step 1: Identify the shape and dimensions. It is a cube with a side length (width) of 9 cm. In a cube, all sides (length, width, height) are equal.
* Step 2: Use the volume formula for a cube: $Volume = side \times side \times side$ ($s^3$).
* Step 3: Calculate: $9 \times 9 \times 9$.
* $9 \times 9 = 81$
* $81 \times 9 = 729$
* Step 4: The unit is cubic centimeters ($cm^3$).
* Result: $729 \text{ cm}^3$.
*(Note: The answer key in the image lists "729 mm³", which appears to be a typo in the original document since the input was in cm. The correct mathematical answer based on the text is cm³.)*

2) A rectangular prism has a width of 2 cm, a height of 9 cm and a depth of 6 cm. What is the volume of the prism?
* Step 1: Identify dimensions: Width = 2 cm, Height = 9 cm, Depth (Length) = 6 cm.
* Step 2: Use the volume formula for a rectangular prism: $Volume = Length \times Width \times Height$.
* Step 3: Calculate: $6 \times 2 \times 9$.
* $6 \times 2 = 12$
* $12 \times 9 = 108$
* Step 4: The unit is cubic centimeters ($cm^3$).
* Result: $108 \text{ cm}^3$.
*(Note: The answer key in the image lists "108 ft³", which is a typo in the original document. The input was in cm, so the output should be cm³.)*

3) A rectangular prism has a width of 4 cm, a height of 2 cm and a depth of 9 cm. What is the volume of the prism?
* Step 1: Identify dimensions: Width = 4 cm, Height = 2 cm, Depth = 9 cm.
* Step 2: Formula: $Volume = Length \times Width \times Height$.
* Step 3: Calculate: $9 \times 4 \times 2$.
* $9 \times 4 = 36$
* $36 \times 2 = 72$
* Step 4: The unit is cubic centimeters ($cm^3$).
* Result: $72 \text{ cm}^3$.
*(Note: The answer key in the image lists "72 in³", which is a typo in the original document. The input was in cm.)*

4) A cube has depth of 6 cm. What is the volume of the cube?
* Step 1: Identify shape and dimension. Cube with side length 6 cm.
* Step 2: Formula: $Volume = s^3$.
* Step 3: Calculate: $6 \times 6 \times 6$.
* $6 \times 6 = 36$
* $36 \times 6 = 216$
* Step 4: The unit is cubic centimeters ($cm^3$).
* Result: $216 \text{ cm}^3$.
*(Note: The answer key in the image lists "216 ft³", which is a typo in the original document. The input was in cm.)*

5) A rectangular prism has a width of 7 cm, a height of 8 cm and a depth of 9 cm. What is the volume of the prism?
* Step 1: Identify dimensions: Width = 7 cm, Height = 8 cm, Depth = 9 cm.
* Step 2: Formula: $Volume = Length \times Width \times Height$.
* Step 3: Calculate: $9 \times 7 \times 8$.
* $9 \times 7 = 63$
* $63 \times 8 = 504$
* Step 4: The unit is cubic centimeters ($cm^3$).
* Result: $504 \text{ cm}^3$.
*(Note: The answer key in the image lists "504 in³", which is a typo in the original document. The input was in cm.)*

6) A cube has height of 6 cm. What is the volume of the cube?
* Step 1: Identify shape and dimension. Cube with side length 6 cm.
* Step 2: Formula: $Volume = s^3$.
* Step 3: Calculate: $6 \times 6 \times 6 = 216$.
* Step 4: The unit is cubic centimeters ($cm^3$).
* Result: $216 \text{ cm}^3$.
*(Note: The answer key in the image lists "216 mm³", which is a typo in the original document. The input was in cm.)*

7) What is the volume of a figure with that is 6 inches wide, 6 inches tall and 7 inches long?
* Step 1: Identify dimensions: Width = 6 in, Height = 6 in, Length = 7 in.
* Step 2: Formula: $Volume = Length \times Width \times Height$.
* Step 3: Calculate: $7 \times 6 \times 6$.
* $6 \times 6 = 36$
* $36 \times 7 = 252$
* Step 4: The unit is cubic inches ($in^3$).
* Result: $252 \text{ in}^3$.
*(Note: The answer key in the image lists "252 cm³", which is a typo in the original document. The input was in inches.)*

8) A rectangular prism has a width of 10 cm, a height of 2 cm and a depth of 4 cm. What is the volume of the prism?
* Step 1: Identify dimensions: Width = 10 cm, Height = 2 cm, Depth = 4 cm.
* Step 2: Formula: $Volume = Length \times Width \times Height$.
* Step 3: Calculate: $4 \times 10 \times 2$.
* $4 \times 10 = 40$
* $40 \times 2 = 80$
* Step 4: The unit is cubic centimeters ($cm^3$).
* Result: $80 \text{ cm}^3$.
*(Note: The answer key in the image lists "80 ft³", which is a typo in the original document. The input was in cm.)*

9) A cube has height of 5 cm. What is the volume of the cube?
* Step 1: Identify shape and dimension. Cube with side length 5 cm.
* Step 2: Formula: $Volume = s^3$.
* Step 3: Calculate: $5 \times 5 \times 5$.
* $5 \times 5 = 25$
* $25 \times 5 = 125$
* Step 4: The unit is cubic centimeters ($cm^3$).
* Result: $125 \text{ cm}^3$.

10) What is the volume of a figure with that is 3 inches wide, 3 inches tall and 2 inches long?
* Step 1: Identify dimensions: Width = 3 in, Height = 3 in, Length = 2 in.
* Step 2: Formula: $Volume = Length \times Width \times Height$.
* Step 3: Calculate: $2 \times 3 \times 3$.
* $3 \times 3 = 9$
* $9 \times 2 = 18$
* Step 4: The unit is cubic inches ($in^3$).
* Result: $18 \text{ in}^3$.

Final Answer:
1. 729 cm³
2. 108 cm³
3. 72 cm³
4. 216 cm³
5. 504 cm³
6. 216 cm³
7. 252 in³
8. 80 cm³
9. 125 cm³
10. 18 in³