If you are about to calculate the area of a new house or a particular place, you would have to know how to find surface area of that spot. Finding the surface area is pretty simple if you know the formula and solve it accordingly. But before we go into that, you need to know the concept well. So let us share with you all those details in this article.
As you know, the surface area is the total amount of space that all the surfaces of an object take up. In other words, it is the sum of the area of all surfaces of that object. Therefore, finding the surface area of a three-dimensional shape is moderately easy as long as you know the correct formula. Needless to say, each shape has its own separate formula. Therefore, you first need to identify the shape you are working with before finding the area.
So memorizing the surface area formula for different objects can make calculations easier in the future. Therefore, in today’s article, we discussed how to find the surface area of some of the most common shapes you might encounter. Stay tuned to us to know all these aspects!
What Are The Different Shapes or How To Find Surface Area?
Do you love solving maths problems? Well, then, you might be interested in finding the surface area of different shapes. So in today’s article, we will share some of the easiest ways that you can use to find the surface area. This will also help you calculate the surface area of some of the most common shapes we often encounter. Let us take a look down below:
How To Find Surface Area: Cube
Let us see how we can calculate the surface area of a cube:
- Define The Formula For The Surface Area Of A Cube
One of the first steps you need to follow before finding the surface area of a cube is knowing the formula. As you know, a cube has six identical square sides. Since both the length and width of a square are equal, the area of a square is a2, where a is the length of a side.
As you know, there are six identical sides of a cube, so to find the surface area, simply multiply the area of one side times 6. The formula for a cube’s surface area (SA) is SA = 6a2, where a is the length of one side. Therefore, the surface area units will be some unit of length squared: in2, cm2, m2, etc.
- Measure The Length Of One Side
You must know that each side or edge of a cube should be equal in length to the others. Therefore, you only need to measure one side. So by using a ruler, measure the length of the side and pay attention to the units you are using. Pretty simple, right?
- Square Your Measurement For ‘a’
Square the measurement taken for the length of the edge. So to square, a measurement means to multiply it by itself. Therefore, when you are first learning these formulas, write it as SA = 6* a* a. So this step calculates the area of one side of the cube. For instance, a = 2 cm, a2 = 2×2 = 4 cm2.
- Multiply The Product By Six
As you know, a cube has six identical sides. Now that you know the area of one side, you need to multiply it by six to calculate the area of all six sides. So this step completes the calculation of the cube’s surface area. For instance, a2 = 4 cm2, and the surface area will be 6 x a2 = 6 x 4 = 24 cm2.
How To Find Surface Area: Cone
Now let us see how we can find out the surface area of a cone:
- Define The Surface Area Formula For A Cone
So you must have already developed an idea by now regarding the concept of surface area and how you can calculate it for a cube. Now, let us see how we can find it for a cone. Well, just like the cube, firstly, you need to know the formula of the surface area of a cube.
As you know, a cone has a circular base and a rounded surface that tapers into a point. Therefore, to find the surface area, you need to calculate the circular base and the cone’s surface area. Now add the two together. So the formula for the surface area of a cone is SA = n*r2 + n*rl, where r is the radius of the circular base, l is the slant height of the cone, and 𝜋 is the mathematical constant pi (3.14).
Measure The Radius & Height Of The Cone
As you know, the radius is the distance from the center of the circular base to the side of the base. So the height is the distance from the center of the base to the top peak of the cone, as measured through the center of the cone. Now let us move over to the next step of the calculation.
Calculate The Slant Height (l) Of The Cone
The slant height is nothing but the hypotenuse of a triangle. So you need to use the Pythagoras Theorem to calculate the slant height. Therefore, apply the formula l = √ (r2 + h2), where r is the radius and h is the height of the cone.
Determine The Area Of The Circular Base
So the area of the base is calculated with the formula n*r2. After measuring the radius, square it (multiply it by itself) and then multiply that product by pi. Pretty simple, right? You can follow the above formula to know about the area of the circular base.
Calculate The Surface Area Of The Top Of The Cone
Using the formula n*rl, where r is the radius of the circle and l is the slant height previously calculated, you can find the surface area of the top part of the cone. So now you will be able to find the surface area.
Add Two Areas Together To Find the Total Surface Area
Finally, you have to calculate the cone’s final surface area by adding the circular base area to the calculation from the previous step. So you can easily find out the surface area of the cone by following the above steps.
Ending Note
As we conclude, finding the surface area is pretty easy if you know the right formula. Therefore, if you are thinking about how to find the surface area, you can follow the above article to learn the steps to calculate it for different shapes. We have summed up all the points in a compact way.
