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 ✕ l², where l is the length
• Volume of cube = l³
• Lateral Surface Area of a Cylinder = 2πrh
• Total Surface Area of a Cylinder = 2πr (h+r)
• Volume of Cylinder = πr² h
• Lateral Surface Area of Cone = πrL
• Total surface area of cone = πr ( L+ r)
• Volume of Cone = ⅓ (πr² h)
• Surface Area of Sphere= 4 πr²
• Volume of Sphere = 4/3 (πr³)
• Volume of a frustum of a cone = 1/3 πh(r_₁² + r_₂² + r_₁r_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 cm³ 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 = a³, 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 = a³

Volume of the cube, a³ = 27 cm³

a³ = 27 cm³

a = ∛(27 cm³)

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 cm² + 18 cm² + 18 cm²)

= 2 × 45 cm²

= 90 cm²

Thus, the surface area of the resulting cuboid is 90 cm².

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