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

__Download beautiful PDF of all the Formulas of 3-D solids__**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 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 + 2
**π****(**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 = πr2 + 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 (
**R**2 + 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 Area = 2πR2 + 2πr2+ (
**R**2 – r2) - Volume = 2/3 π (R3 – r3)