Word Problem of Volume worksheet - Free Printable
Educational worksheet: Word Problem of Volume worksheet. Download and print for classroom or home learning activities.
JPG
1000×1291
120.1 KB
Free · Personal Use
Quality Assured by Worksheets Library Team
Reviewed for educational accuracy and age-appropriateness
ID: #1280292
⭐
Show Answer Key & Explanations
Step-by-step solution for: Word Problem of Volume worksheet
▼
Show Answer Key & Explanations
Step-by-step solution for: Word Problem of Volume worksheet
Here are the solutions for the volume problems in the worksheet. I have chosen one problem from each row to solve, showing the step-by-step calculations.
Problem: A cubical water tank has a height of 4 m. How much water can the tank hold?
* Step 1: Identify the shape and formula.
The shape is a cube. The formula for the volume of a cube is $side \times side \times side$ (or $s^3$).
* Step 2: Identify the side length.
Since it is a cube, all sides are equal. The height is given as 4 m, so the length and width are also 4 m.
* Step 3: Calculate the volume.
$$Volume = 4 \times 4 \times 4$$
$$4 \times 4 = 16$$
$$16 \times 4 = 64$$
Answer: 64 m³
---
Problem: A classroom is 26 feet wide, 32 feet long, and 9 feet high. What is the volume of the room in cubic feet?
* Step 1: Identify the formula.
The formula for the volume of a rectangular prism is $Length \times Width \times Height$.
* Step 2: Plug in the numbers.
$$Volume = 32 \times 26 \times 9$$
* Step 3: Calculate.
First, multiply the length by the width:
$$32 \times 26 = 832$$
Next, multiply that result by the height:
$$832 \times 9 = 7,488$$
Answer: 7,488 feet³
---
Problem: The base of a prism is a right triangle with legs measuring 16 feet and 4 feet. If the height of the prism is 14 feet, find its volume.
* Step 1: Find the area of the triangular base.
The formula for the area of a triangle is $\frac{1}{2} \times base \times height$. Here, the "legs" of the right triangle act as the base and height of the triangle itself.
$$Area of Base = \frac{1}{2} \times 16 \times 4$$
$$\frac{1}{2} \times 16 = 8$$
$$8 \times 4 = 32 \text{ square feet}$$
* Step 2: Calculate the volume of the prism.
Multiply the area of the base by the height of the prism (14 feet).
$$Volume = 32 \times 14$$
$$32 \times 10 = 320$$
$$32 \times 4 = 128$$
$$320 + 128 = 448$$
Answer: 448 feet³
---
Problem: Shawn is making a candle using a cylindrical mold with a radius of 2 cm and a height of 30 cm. How many cubic centimeters of wax are needed for the candle?
* Step 1: Identify the formula.
The formula for the volume of a cylinder is $\pi \times r^2 \times h$. We will use $3.14$ for $\pi$.
* Step 2: Square the radius.
$$r = 2$$
$$2^2 = 2 \times 2 = 4$$
* Step 3: Multiply by pi and height.
$$Volume = 3.14 \times 4 \times 30$$
First, multiply $3.14 \times 4$:
$$3.14 \times 4 = 12.56$$
Next, multiply by the height (30):
$$12.56 \times 30 = 376.8$$
Answer: 376.8 cm³
---
Problem: A rectangular pyramid has a length of 22 inches, a width of 18 inches and a height of 12 inches. Determine the volume of the pyramid.
* Step 1: Identify the formula.
The formula for the volume of a pyramid is $\frac{1}{3} \times Length \times Width \times Height$.
* Step 2: Plug in the numbers.
$$Volume = \frac{1}{3} \times 22 \times 18 \times 12$$
* Step 3: Calculate.
It is often easier to divide by 3 first if possible. Let's look at $18 \div 3 = 6$ or $12 \div 3 = 4$. Let's divide 12 by 3.
$$Volume = 22 \times 18 \times 4$$
First, multiply $22 \times 18$:
$$22 \times 18 = 396$$
Next, multiply by 4:
$$396 \times 4 = 1,584$$
Answer: 1,588 inc³ *(Correction during check: $396 \times 4 = 1584$)* -> 1,584 inc³
Final Answer:
Cube: 64 m³
Rectangular Prism: 7,488 feet³
Triangular Prism: 448 feet³
Cylinder: 376.8 cm³
Pyramid: 1,584 inc³
1. Cube (Problem A)
Problem: A cubical water tank has a height of 4 m. How much water can the tank hold?
* Step 1: Identify the shape and formula.
The shape is a cube. The formula for the volume of a cube is $side \times side \times side$ (or $s^3$).
* Step 2: Identify the side length.
Since it is a cube, all sides are equal. The height is given as 4 m, so the length and width are also 4 m.
* Step 3: Calculate the volume.
$$Volume = 4 \times 4 \times 4$$
$$4 \times 4 = 16$$
$$16 \times 4 = 64$$
Answer: 64 m³
---
2. Rectangular Prism (Problem A)
Problem: A classroom is 26 feet wide, 32 feet long, and 9 feet high. What is the volume of the room in cubic feet?
* Step 1: Identify the formula.
The formula for the volume of a rectangular prism is $Length \times Width \times Height$.
* Step 2: Plug in the numbers.
$$Volume = 32 \times 26 \times 9$$
* Step 3: Calculate.
First, multiply the length by the width:
$$32 \times 26 = 832$$
Next, multiply that result by the height:
$$832 \times 9 = 7,488$$
Answer: 7,488 feet³
---
3. Triangular Prism (Problem A)
Problem: The base of a prism is a right triangle with legs measuring 16 feet and 4 feet. If the height of the prism is 14 feet, find its volume.
* Step 1: Find the area of the triangular base.
The formula for the area of a triangle is $\frac{1}{2} \times base \times height$. Here, the "legs" of the right triangle act as the base and height of the triangle itself.
$$Area of Base = \frac{1}{2} \times 16 \times 4$$
$$\frac{1}{2} \times 16 = 8$$
$$8 \times 4 = 32 \text{ square feet}$$
* Step 2: Calculate the volume of the prism.
Multiply the area of the base by the height of the prism (14 feet).
$$Volume = 32 \times 14$$
$$32 \times 10 = 320$$
$$32 \times 4 = 128$$
$$320 + 128 = 448$$
Answer: 448 feet³
---
4. Cylinder (Problem A)
Problem: Shawn is making a candle using a cylindrical mold with a radius of 2 cm and a height of 30 cm. How many cubic centimeters of wax are needed for the candle?
* Step 1: Identify the formula.
The formula for the volume of a cylinder is $\pi \times r^2 \times h$. We will use $3.14$ for $\pi$.
* Step 2: Square the radius.
$$r = 2$$
$$2^2 = 2 \times 2 = 4$$
* Step 3: Multiply by pi and height.
$$Volume = 3.14 \times 4 \times 30$$
First, multiply $3.14 \times 4$:
$$3.14 \times 4 = 12.56$$
Next, multiply by the height (30):
$$12.56 \times 30 = 376.8$$
Answer: 376.8 cm³
---
5. Pyramid (Problem A)
Problem: A rectangular pyramid has a length of 22 inches, a width of 18 inches and a height of 12 inches. Determine the volume of the pyramid.
* Step 1: Identify the formula.
The formula for the volume of a pyramid is $\frac{1}{3} \times Length \times Width \times Height$.
* Step 2: Plug in the numbers.
$$Volume = \frac{1}{3} \times 22 \times 18 \times 12$$
* Step 3: Calculate.
It is often easier to divide by 3 first if possible. Let's look at $18 \div 3 = 6$ or $12 \div 3 = 4$. Let's divide 12 by 3.
$$Volume = 22 \times 18 \times 4$$
First, multiply $22 \times 18$:
$$22 \times 18 = 396$$
Next, multiply by 4:
$$396 \times 4 = 1,584$$
Answer: 1,588 inc³ *(Correction during check: $396 \times 4 = 1584$)* -> 1,584 inc³
Final Answer:
Cube: 64 m³
Rectangular Prism: 7,488 feet³
Triangular Prism: 448 feet³
Cylinder: 376.8 cm³
Pyramid: 1,584 inc³
Parent Tip: Review the logic above to help your child master the concept of volume of rectangular prism worksheet word problems.
