Are you confused about the surfaces of solids? You landed on the correct page where you will get plenty of knowledge on the surfaces of solids. This article explains the definition of surfaces of solids, Types of Surfaces, How to find the surfaces of regular solids, surfaces of irregular solids. Check out the regular solids surface area formulas in the later modules.

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## Surface Area of Solids – Definition

The measurement ofÂ the entireÂ area that the surface ofÂ the thingÂ occupiesÂ of a solid object.

When we check outÂ the shapes,Â we discoverÂ that some are flatÂ and a fewÂ are curved. These facesÂ aren’tÂ only seen butÂ also canÂ be touched. This is known as the surfaces of the solids or 3-D figures. Surface area can be measured in square units.

There are two sorts ofÂ surfaces: (i) Total surface area and (ii) Curved surface

### Total Surface Area

Total surface area means the area including the base and the curved part. It means the total area covered by the surface of the object. If the object has both a curved surface and base, then the total area will be the sum of the two areas.

### Curved Surface Area/Lateral Surface Area

The surfaces which aren’tÂ flat, are called curved surface. Curved surface area refers to the area of the curved part of the shape and not it’s base. It is also known as Lateral surface area.

The surface of a ball, or an apple, or orange are examples of curved or maybe a spherical surface. Spherical surfaces are formed by just oneÂ surface. We can observe some objects which have both plane and curved sorts ofÂ surfaces. For example, drums and clocks are such objects having both flat and curved surfaces.

Regular solids have definite formulas for locatingÂ their surface areas. We know the examples of regular solids which include cubes, prisms, cuboids, spheres, hemispheres, cones, and cylinders.

### Surface Area of the Regular Solids

Here we will find out the surface areas of the regular solids. We have listed the formulas for finding the surface area of regular solids in the below modules. They are as such

### Area of a Solid Cube

TheÂ areaÂ of a solid cube = 4s^{2}

Where s = length of the side.

### Surface Area of a Cuboid

The Cuboid Surface area = 2lw + 2lh + 2wh

SA = 2(lw + lh + wh)

Where, l = length of cuboid, w = width of cuboid, and h = height of the cuboid.

### Surface Area of a Solid Prism

A prismÂ may be aÂ three-dimensional solid with two parallel and congruent polygonal bases connected by rectangular faces. The formula for theÂ areaÂ for a prism depends onÂ the formÂ of its base.

The general formula for theÂ areaÂ of a prism = 2 Ã— area ofÂ the bottomÂ + perimeter of base Ã— height.

SA = 2B + ph

### Surface Area of a Solid Cylinder

A solid cylinder is an object which has two parallel circular bases and they are joined by a curved surface, at a fixed distance from the center.

TheÂ areaÂ of a cylinder = 2 Ã— area of circle + area of a rectangle (the curved surface)

The solid cylinder surface area = 2Ï€r (r + h)

### Surface Area of a Solid Cone

A cone is solid with a circular base connected to a curved surface that tapers fromÂ the bottomÂ toÂ the highest.

The surface area of a solid cone = Area of sector + area of a circle

SA =Ï€rs + Ï€r^{2} = Ï€r (r + s)

Where sÂ is that theÂ slant height of a cone and rÂ is that theÂ radius of the circular base.

### Surface Area of a Solid Pyramid

A pyramidÂ is often defined as a solid with a polygonal base and triangular lateral faces.Â a bit likeÂ a prism, a pyramidÂ is known asÂ after the formÂ of its base.

The general formula for theÂ areaÂ of a solid pyramid is:

SA = Base area + Â½ ps

Where p = perimeter ofÂ and s = slant height of a pyramid.

For, a square pyramid, the, SA = b^{2} + 2bs

Where, b = base length of the square pyramid and s = slant height of the square pyramid.

### Surface Area of a Solid Sphere

TheÂ areaÂ of a sphere, SA = 4 Ï€r^{2}

For a solid hemisphere, theÂ area, SA = 3Ï€r^{2}

### The Surface Area of Irregular Solids

An irregular objectÂ may be aÂ combination of two or more regular objects. Therefore, theÂ areaÂ of irregular solidÂ is often calculated by adding together the regular objectsâ€™ surface areas that form it.

### FAQs on the Surface of Solids

**1. What is the formula for the total surface area of the cylinder?**

The total surface area of the cylinder = 2 Ï€ r(r+h), where r is the radius of the circular base and h is the height of the cylinder.

**2. What is the Surface area of the cone?**

The surface area of a solid cone = Area of sector + area of a circle

SA =Ï€rs + Ï€r^{2} = Ï€r (r + s)

Wheres is that theÂ slant height of a cone and rÂ is that theÂ radius of the circular base.

**3. Find the total surface area of the hemisphere?**

The total surface area of the hemisphere is equal to the sum of half of the surface area of the sphere and the area of its circular base.

Total surface area of hemisphere = 2 Ï€ r^{2}+ Ï€ r^{2}Â = 3 Ï€ r^{2}

**4. What is the area of the prism?**

The area of a prism = 2 Ã— area of the bottom + perimeter of base Ã— height.

SA = 2B + ph