# Surface Area and Volume Class 10 Formulas

Surface Area and Volume class 10 formulas help students to study various dimensions of different solid shapes like cube, cone, cylinder, cuboid, etc. As these concepts are a part of our everyday life, students need to efficiently memorize these surface area and volume class 10 formulas along with formulas of solid figures studied in previous grades.

## List of Surface Area and Volume Class 10 Formulas

Here is a list of the Surface Area and Volume formulas for class 10.

- Surface Area of a cuboid of length (l), breadth (b), and height (h) = 2 (lb + bh + lh)
- Lateral Surface Area of cuboid = 2 (l + b)h
- Surface Area of a cube = 6 ✕ l2 where l is the length
- Lateral Surface Area of cube = 4 ✕ l
^{2}, where l is the length - Volume of cube = l
^{3} - Lateral Surface Area of a Cylinder = 2πrh
- Total Surface Area of a Cylinder = 2πr (h+r)
- Volume of Cylinder = πr
^{2}h - Lateral Surface Area of Cone = πrL
- Total surface area of cone = πr ( L+ r)
- Volume of Cone = ⅓ (πr
^{2}h) - Surface Area of Sphere= 4 πr
^{2} - Volume of Sphere = 4/3 (πr
^{3}) - Volume of a frustum of a cone = 1/3 πh(r
_{₁}^{2}+ r_{₂}^{2}+ r_{₁}r_{₂})

## Applications of Surface Area and Volume Class 10 Formulas

Here are some of the applications of surface area and volume class 10 formulas:

- Surface area and volume class 10 formulas are used for finding out things that are proportional to the surface area and volume. For example, to determine the quantity of paint that would be needed to cover the object or the amount of wallpaper that would be required to cover a wall.
- Surface area and volume formulas are utilized in cooking to measure the ingredients in the various recipes.
- These formulas are applied in many routine calculations like determining the amount of fuel to fill a car's tank or for adding detergent to the washing machine.
- Surface area formulas are often used in electronics to design circuit boards.
- These formulas are also applied to calculate the cost of an apartment/house based on the price per square feet.
- Construction and architectural works, material estimating, pattern layout, programming, budgeting, site design, code analyses, etc. are some of the other fields where Surface area and volume formulas are widely applied.

## Tips to Memorize Surface Area and Volume Class 10 Formulas

Here are some tips that could be helpful for kids to memorize Surface area and volume formulas for class 10.

- The students must make sure to understand the concepts first before moving ahead to memorize the formulas. They should also clear their doubts and seek help from their teachers to form a clear understanding of each concept.
- They can also go through the derivation of these formulas to develop a rock-solid foundation as well as understand the underlying concepts.
- It is necessary that the students must practice a variety of questions based on surface area and volume formulas to ensure a thorough conceptual understanding of all important formulas.

## Surface Area and Volume Class 10 Formulas Examples

**Example: **Two cubes with volume 27 cm^{3} are joined back-to-back with each other. Determine the surface area of the cuboid formed.

**Solution:** Let’s determine the length of the edge of each cube by applying the volume of the cube formula. The volume of a cube = a^{3}, where the length of the edge is 'a'.

Using the formula for the surface area of a cuboid = 2(lb + bh + lh), where l, b, and h are length, breadth, and height respectively.

Let the length of the edge of each cube be 'a'

Therefore, volume of the cube = a^{3}

Volume of the cube, a^{3} = 27 cm^{3}

a^{3} = 27 cm^{3}

a = ∛(27 cm^{3})

a = 3 cm

Therefore,

Length of the resulting cuboid, l = a = 3 cm

Breadth of the resulting cuboid, b = a = 3 cm

Height of the resulting cuboid, h = 2a = 2 × 3 cm = 6 cm

Surface area of the resulting cuboid = 2 (lb + bh + lh)

= 2 (3 cm × 3 cm + 3 cm × 6 cm + 3 cm × 6 cm)

= 2 (9 cm^{2} + 18 cm^{2} + 18 cm^{2})

= 2 × 45 cm^{2}

= 90 cm^{2}

Thus, the surface area of the resulting cuboid is 90 cm^{2}.

Students can download the printable **Maths Formulas Class 10** sheet from the link provided below:

## FAQs on Surface Area and Volume Class 10 Formulas

### What are the Important Surface Area and Volume class 10 formulas?

Here are important Surface Area and Volume Class 10 formulas that students need to remember in order to solve the questions related to the topic.

- Surface Area of a cuboid of length (l), breadth (b), and height (h) = 2 (lb + bh + lh)
- Lateral Surface Area of cuboid = 2 ( l+ b) h
- Surface Area of a cube = 6 x l2 where l is the length
- Lateral Surface Area of cube = 4 x l
^{2}, where l is the length - Volume of cube = l
^{3} - Lateral Surface Area of a Cylinder = 2πrh
- Total Surface Area of a Cylinder = 2πr (h+r)
- Volume of Cylinder = πr
^{2}h - Lateral Surface Area of Cone = πrL
- Total surface area of cone = πr ( L+ r)
- Volume of Cone = ⅓ (πr
^{2}h) - Surface Area of Sphere= 4 πr
^{2} - Volume of Sphere = 4/3 (πr
^{3})

### How Many Formulas are There in Surface Area and Volume Class 10?

There is a long list of important formulas based on surface area and volume of different shapes like cube, cuboid, cylinder, hemisphere, cone, etc. Most of the questions covered in this chapter are based on formulas; therefore, it is necessary to memorize them. Besides, students should also learn to derive each of these formulas. It will benefit them to understand the solutions to all the questions with ease.

### Why Should Students Practice Questions Based on Surface Area and Volume Class 10 Formulas?

Maths is all about practice and students must practice maximum questions based on Surface Area and Volume Class 10 Formulas. Solving all types of problems based on these formulas will help students understand key concepts and explore their applications. Getting well-versed with the concepts will enable students to identify and derive different formulas which are to be applied in the questions.

### How to Memorize Surface Area and Volume Class 10 Formulas?

One of the most effective ways to learn and memorize surface area and volume class 10 formulas is to apply them in solving various types of problems. While applying these formulas students will be able to understand and derive them. It will be helpful for them to quickly revise them during exams.

### How to Download Surface Area and Volume Formulas Class 10 pdf?

Students can easily download the surface area and volume formulas class 10 pdf by clicking on the download option provided on the page. On clicking the option, a popup will appear. Students need to provide a valid phone number to receive an OTP. Once the OTP is entered the pdf file will automatically download on the device.

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