In this article, we’ll explore the concepts of Surface area and volume for Class 10 students. We’ll cover various geometric shapes, including the cube, cuboid, cone, cylinder, and more. Surface area can be classified into Lateral Surface Area (LSA), Total Surface Area (TSA), and Curved Surface Area (CSA).

Here, let us discuss the surface area formulas and volume formulas for different three-dimensional shapes in detail.

Rectangular Prism (Cuboid):

• Volume (V) = Length (l) × Width (w) × Height (h)
• Surface Area (SA) = 2lw + 2lh + 2wh

Cube:

• Volume (V) = Side length (s)^3
• Surface Area (SA) = 6s^2

Cylinder:

• Volume (V) = πr^2h (where r is the radius and h is the height)
• Curved Surface Area (CSA) = 2πrh
• Total Surface Area (TSA) = 2πr^2 + 2πrh

Sphere:

• Volume (V) = (4/3)πr^3 (where r is the radius)
• Surface Area (SA) = 4πr^2

Cone:

• Volume (V) = (1/3)πr^2h (where r is the radius and h is the height)
• Curved Surface Area (CSA) = πr√(r^2 + h^2)
• Total Surface Area (TSA) = πr(r + √(r^2 + h^2))

Pyramid (Regular):

• Volume (V) = (1/3) × Base Area (B) × Height (h)
• Surface Area (SA) = (1/2) × Perimeter of Base (P) × Slant Height (l) + B (base area)

Frustum

• Curved Surface Area = π(r ₁ + r ₂ )l
• Total Surface Area =π(r ₁ + r ₂ )l + πr ₁ ²  + πr ₂ ²
• Volume = 1/3 πh (r ₁ ² + r ₂ ² + r ₁ r ₂ )

Prism (Regular):

• Volume (V) = Base Area (B) × Height (h)
• Surface Area (SA) = 2B + Ph (where P is the perimeter of the base)

Hemisphere:

• Volume (V) = (2/3)πr^3 (where r is the radius)
• Curved Surface Area (CSA) = 2πr^2
• Total Surface Area (TSA) = 3πr^2

Triangular Prism:

• Volume (V) = (1/2) × Base Area (B) × Height (h)
• Surface Area (SA) = 2B + Ph (where P is the perimeter of the base)

Cylinder with an open top (Hollow Cylinder):

Volume (V) = πh(R^2 – r^2) (where R is the outer radius, r is the inner radius, and h is the height) – Curved Surface Area (CSA) = 2πh(R + r) – Total Surface Area (TSA) = 2πh(R + r) + 2π(R^2 – r^2)