Volume of a Cone Worksheet Answers for Students (All Grades)

Have you ever looked at an ice cream cone and wondered how much space is inside it? That space is called volume. In geometry we learn volume for many shapes. One of the most interesting shapes is a cone. Students often learn this topic in Grade 7 Grade 8 and Grade 9.

Today we will learn volume of a cone in a simple way with worksheet questions and answers.

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Volume of a Cone Worksheet Answers

A cone has a round flat base and a pointed top. To find how much space is inside the cone we use a formula. We call this the volume of a cone.

Real life cone examples:

1. Ice cream cone
2. Traffic cone
3. Party hat
4. Funnel

These shapes help us understand cone volume in a fun way.

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Volume of a Cone Formula

The formula is very easy.

V = 1/3 π r² h

V means volume
r means radius of base
h means height of cone
π is a special number we read as pi
We use 3.14 or 22/7 for pi in school problems

We multiply area of the circle r² by height h then divide by 3.

Steps to Solve a Volume Problem

1. Check if radius is given
2. If diameter is given divide by 2 to get radius
3. Put values in formula V = 1/3 π r² h
4. Multiply numbers step by step
5. Write cubic units in answer like cm³ or m³

Is it easy? Yes with practice you will enjoy it.

Worksheet Questions and Answers

Here are practice questions with answers. These help students learn and check mistakes.

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Worksheet 1: Basic Problems

Q1. Radius r = 3 cm height h = 6 cm
Find volume
Answer
V = 1/3 × 3.14 × 3² × 6
V = 1/3 × 3.14 × 9 × 6
V = 56.52 cm³

Q2. Radius r = 5 m height h = 12 m
Answer
V = 1/3 × 3.14 × 25 × 12
V = 314 m³

Q3. Radius r = 4 cm height h = 10 cm
Answer
V = 1/3 × 3.14 × 16 × 10
V = 167.47 cm³

Worksheet 2: Diameter Problems

Remember
Diameter ÷ 2 = Radius

Q4. Diameter = 10 cm height = 15 cm
Radius r = 5 cm
V = 1/3 × 3.14 × 25 × 15
V = 392.5 cm³

Q5. Diameter = 8 m height = 9 m
Radius r = 4 m
V = 1/3 × 3.14 × 16 × 9
V = 150.72 m³

Worksheet 3: Word Problems

Q6. An ice cream cone has radius 4 cm height 7 cm
Find volume
V = 1/3 × 3.14 × 16 × 7
V = 117.02 cm³

Q7. A party cone has radius 6 cm height 20 cm
V = 1/3 × 3.14 × 36 × 20
V = 753.6 cm³

Q8. A funnel has diameter 12 cm height 18 cm
Radius = 6 cm
V = 1/3 × 3.14 × 36 × 18
V = 678.24 cm³

Worksheet 4: Compare Cone and Cylinder

Cylinder formula
V = π r² h
Cone volume is only one third of cylinder with same base and height

Q9. Radius = 3 cm height = 9 cm
Cylinder Volume
= 3.14 × 9 × 9 = 254.34 cm³
Cone Volume
= 1/3 × 254.34 = 84.78 cm³

This shows cone volume is smaller.

Conclusion

Learning the volume of a cone can be simple and fun. When students solve worksheets every day they become stronger in geometry. Practice helps you remember the formula and solve real life cone questions.

Now try creating your own cone problems. You will enjoy the feeling of finding the right answer.