# Surface Area Formulas and Volume Formulas of 3-D Solids

The meaning of 3-D solids is 3 dimensional solids. In Geometry, a three dimensional shape is defined as a shape or solid having three dimensions- length, breadth (or width) and height (or depth). They have volume. Students can also download the HD printout of Surface Area Formulas and Volume Formulas of 3-D Solids and can stick on their pinboard. This will help them to revise and learn all the formulas for doing sums on 3 d shapes.

## Surface Area Formulas and Volume Formulas of 3-D Solids

Few example of 3-D shapes are cuboid, cube, cone, cylinder, sphere, hemisphere. Below are the formulas for surface area and volume of 3-d solids.

## Surface Area and Volume Formulas of Cuboid

Cuboid is a solid bounded by 6 rectangular plane surfaces.
If l be the length of the cuboid, b its breadth, h be the height and d be the diagonal, then
• Diagonal = (l2 +b2 + h2)
• Lateral Surface Area/ Area of 4 walls = 2h (l +b)
• Total Surface Area = (lb + bh + hl)
• Volume = l x b x h

## Surface Area and Volume Formulas of Cube

Cube is a solid bounded by 6 square plane surfaces.
If a be the edge of the cube, and d be the diagonal, then
• Diagonal = (3)a
• Lateral Surface Area/ Area of 4 walls = 4a2
• Total Surface Area = 6a2
• Volume = a3

## Surface Area and Volume Formulas of Cylinder

A solid obtained by revolving a rectangular lamina about one of its sides is called a right circular cylinder. The cross sections of a cylinder are two congruent circles. Below are the formulas for surface area and volume of a solid cylinder and a hollow cylinder.

### Surface area and volume of  Solid Cylinder

Let r be the radius and h be the height of a solid cylinder, then
• Circumference of base = 2πr
• Area of base = πr2
• Curved Surface area = 2πrh
• Total Surface Area = 2πr2 + 2πrh
• Volume = πr2h

### Surface area and volume of  Hollow Cylinder

Let R and r be the external and internal radii of a hollow cylinder and h be the height, then

• Thickness of cylinder = R – r
• Area of circular ring (cross-section) = π (R2 _ r2)
• External Curved Surface area = 2πRh
• Internal Curved Surface area = 2πrh
• Total Surface Area = 2πRh + 2πrh + 2π (R2 _ r2)
• Volume of the material = πh (R2 _ r2)

## Surface Area and Volume Formulas of Cone

A solid obtained by revolving a right angled triangular lamina about any side (other than the hypotenuse) is called a right circular cone. Below are the formulas for surface area and volume of a cone.
Let r be the radius, h be the height and l be the slant height of the cone, then

• Slant height (l) = (h2   + r2)
• Area of Base = πr2
• Curved (lateral) surface area = πrl
• Total Surface Area = πr+ πrl

## Surface Area and Volume Formulas of Sphere

A sphere is a three dimensional figure, which is made up of all points in space that lie at a constant distance from a fixed point. The constant distance is called radius and the fixed point is called the centre of the sphere.

### Surface Area and Volume Formulas of a Solid Sphere

Let r be the radius of the solid sphere, then
• Surface Area = 4πr2
• Volume = 4/3 πr3

### Surface Area and Volume Formulas of a Spherical Shell

Let R and r be the external and internal radii of a spherical shell, then

• Thickness of shell = R – r
• Surface Area = 4π (R2   + r2)
• Volume = 4/3 π (R3 – r3)

## Surface Area and Volume Formulas of a Hemisphere

When a sphere is cut by a plane passing through its centre, then the sphere is divided into two equal parts. Each part is called a hemisphere.
Let r be the radius of the hemisphere, then
• Curved Surface Area = 2πr2
• Total Surface Area = 3πr2
• Volume = 2/3 πr3

### Surface Area and Volume Formulas of a Hemipherical Shell

Let R and r be the external and internal radii of a Hemispherical shell, then

• Thickness of shell = R – r
• Area of base
• External Curved Surface Area  2πR2
• Internal Curved Surface Area  2πr2
• Total Surface Area2πR2πr2(R2 – r2)
• Volume = 2/3 π (R3 – r3)

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