Humans usually see solids everywhere we look. Thus far, we’ve only dealt with figures that can be easily drawn on our notebooks or blackboards. These would be known as plane figures. We now know what rectangles, squares, and circles are, what their perimeters and areas are, and how to find them. These were taught to us in previous classes. It would be interesting to see what happens if we cut out a large number of these plane figures in the same shape and size from a cardboard sheet and stack them vertically. We will obtain some solid figures (also known as solids) as a result of this process, such as a cuboid, a cylinder, and so on. You’ve also learned how to calculate the surface areas and volumes of cuboids, cubes, and cylinders in previous classes. We will now check how to calculate the surface areas and volumes of cuboids and cylinders in detail, as well as apply this knowledge to other solids such as cones and spheres.
Three-dimensional objects abound in our world. For any visible or touchable object, three dimensions can be measured: length, width, and height. We live in a house that has specific dimensions. The width and length of the rectangular display screen/Monitor you’re looking at are the same. There are two definitions that you must understand when it comes to knowing the volume and surface area of these objects. Surface area is indeed the total area of an object’s outer facing surfaces. The total surface area is calculated by adding all the areas on the surface: the areas of the object’s base, top, and lateral surfaces (sides). This is accomplished by employing various area formulas and measuring in square units. Now, when speaking about volume, it actually refers to the amount of space occupied by a three-dimensional object. There are also formulas for various three-dimensional shapes. An object’s total volume is measured in cubic units.
In fact, the surface area of any given object is the area or zone covered by the object’s surface whereas volume is the amount of space available in an object.
Any three-dimensional (3D) geometrical shape can have its surface area and volume calculated. The surface of any area is the region occupied by an object’s surface and the volume of such an object is the amount of space it has. We have various shapes such as a hemisphere, sphere, cube, cuboid, cylinder, and so on. Each and every three-dimensional shape has an area and a volume. However, two-dimensional shapes such as squares, rectangles, triangles, circles, and so on. We can only measure the area in two dimensions. The surface area of a three-dimensional object is the area occupied by its outer surface. It is expressed in square units.
There are two types of areas:
(1) Total surface area:
The overall surface area is the area that includes the base(s) and the curved portion. It really is the area enclosed by the surface of the object. If the form has a curved base and surface, the total area is the sum of the two regions. Total Surface Area is identified as “the total area covered by an object, including its base and curved part.” When an object has both a base and a curved area, the total surface area is equal to the sum of the two.” We can say that the total surface area of an object is the total area occupied by the object. Consider the cuboid, which has six faces, twelve edges, and eight vertices. The total surface area of the specific shape will be the sum of those six areas.
(2) Curved surface area/Lateral surface area:
Except for its centre, the curved surface area corresponds to the area of only the curved portion of the shape (s). It is frequently referred to as the lateral surface area for shapes such as a cone. A Lateral Surface Area is identified as “the area that includes only the curved surface area of an object or the lateral surface area of an object while excluding the object’s base area.” The Curved Surface Area is another name for the Lateral Surface Area. The curved surface area is referred to by the majority of the Shapes or Objects; the lateral surface area is referred to by the shape or object-like cylinder. That is, “the visible area is referred to as a lateral surface area.”
The volume of a 3D object is the sufficient space it occupies. In general, volume refers to the total amount of space that an object or substance occupies. It is expressed in cubic units.
Surface Area Formulas:
The surface area of a cube is said to be 6s², where s is the length of aside.
The surface area of a rectangular prism is said to be 2(wl + hl + hw), where w is the width, h is the height, and l is the length.
The surface area of a sphere is said to be 4πr², where r is the radius of the sphere.
The surface area of a cylinder is said to be 2πrh + 2πr², where r is the radius of the cylinder and height is the height.
The surface area of a cone is said to be πrs + πr², where r is the radius of the cone and s is the slant.
Volume Formulas:
The volume of a cube is said to be s³, where s is the length of aside.
The volume of a rectangular prism is said to be wlh, where w is the width, h is the height, and l is the length.
The volume of a sphere is said to be (4πr³) / 3, where r is the radius of the sphere.
The volume of a cylinder is said to be πr²h, where r is the radius of the cylinder and height is the height.
The volume of a cone is said to be (πr²h) / 3, where r is the radius of the cone and s is the slant.
All around us, we may notice a variety of solid shapes. We can calculate the surface area and volume of various solid shapes using specific formulas. It is possible to use a cube, cuboids, cylinders, cones, and other solid bodies. There are numerous real-life applications for calculating the surface area or volume of a shape, such as the amount of water required to fill a pool (rectangular prism) or the amount of wrapping paper required to wrap a candle (cylinder) or basketball (sphere). There really are formulas for the most common shapes.
Also Check
The surface area is really the amount of external space that surrounds a three-dimensional shape. A solid shape's volume is the amount of space it takes up. It is the space bounded by a boundary, occupied by an object, or capable of holding something.
Only when we know the dimensions of the solids, we could use formulas to easily find the surface area and volume of the solids.
For three-dimensional shapes, there really are two types of surface areas: total surface area and curved/lateral surface area. The total surface area covers the area of all of the shape's faces, whereas the curved or lateral area only includes the area of the shape's side faces.
