CBSE 10 Mensuration: A Beginner’s Guide to Surface Areas and Volumes (List of Formulas)

In this article, you will delve into the fundamental concepts of surface areas and volumes, and be provided comprehensive information and detailed explanations.

What is surface area?

Surface area is the measure of the total area that the surface of a three-dimensional object occupies. When we calculate the surface area of a three-dimensional object, we find the sum of the areas of all its faces.

Total surface area

The total surface area of an object is the sum of the areas of all its faces, including its bases (if it has any). For example, the total surface area of a cuboid is given by the formula:

TSA = 2(lw + wh + lh)

where l, w, and h are the length, width, and height of the cuboid, respectively.

Curved surface area/lateral surface area

The curved surface area, also known as the lateral surface area, is the measure of the area that only covers the sides of an object. For example, the lateral surface area of a cylinder is given by the formula:

LSA = 2πrh

where r is the radius of the base and h is the height of the cylinder.

What is volume?

Volume is the measure of the amount of space that a three-dimensional object occupies. When we calculate the volume of an object, we find the amount of space that it can hold.

Surface area and volume formulas

There are several surface area and volume formulas that you need to know for CBSE 10. Here are a few examples:

Cuboid

• Volume: V = lwh
• Total surface area: TSA = 2(lw + wh + lh)

Cylinder

• Volume: V = πr²h
• Lateral surface area: LSA = 2πrh
• Total surface area: TSA = 2πr(h + r)

Cone

• Volume: V = 1/3πr^2h
• Lateral surface area: LSA = πr√(r² + h²)
• Total surface area: TSA = πr(r + √(r² + h²))

Solved examples

Let's look at a few examples to help you understand how to apply these formulas:

Example 1:

Find the total surface area of a cuboid with length 5 cm, width 4 cm, and height 3 cm.‍

✅  Solution: TSA = 2(lw + wh + lh) = 2(5 * 4 + 4 * 3 + 3 * 5) = 2(20 + 12 + 15) = 94 cm².

Example 2:

Find the volume of a cylinder with radius 4 cm and height 6 cm.‍

✅  Solution: V = πr²hV = π * 4² * 6 = 96π cm³.

Practice questions on surface areas and volumes

Here are some practice questions to help you sharpen your skills on surface areas and volumes:

• Find the surface area of a cube with edge length 4 cm.
• Find the volume of a cone with radius 3 cm and height 5 cm.
• Find the total surface area of a cylinder with radius 2.5 cm and height 6 cm.

FAQs

What are the formulas for surface area and volume of cuboid?

The volume of a cuboid is given by the formula V = lwh. The total surface area of a cuboid is given by the formula TSA = 2(lw + wh + lh).

What is the total surface area of the cylinder?

The total surface area of a cylinder is given by the formula TSA = 2πr(h + r).

How to calculate the volume of a cone-shaped object?

The volume of a cone-shaped object is given by the formula V = 1/3πr²h.

What is the total surface area of the hemisphere?

The total surface area of a hemisphere is given by the formula TSA = 3πr².

Conclusion

Surface areas and volumes are important concepts in CBSE 10, and mastering them will help you understand the world around you. By following the formulas and examples provided in this article, you can hone your skills and feel confident in your ability to tackle any problem related to surface areas and volumes. For more information and resources on mathematics, visit Aha AI.

Relevant links

• CBSE 10 - Statistics and Probability - Statistics
• Surface Area and Volume Formulas by BYJU's
• NCERT Solutions for Class 10 Mathematics - Surface Areas and Volumes
• Surface Areas and Volumes by Khan Academy