Xael doesn't like sharing her chocolate truffles with anyone. When she receives a box of Lindt truffles, she proceeds to calculate the surface area of each truffle in order to determine the total surface area she has to lick to decrease the probability that anyone will try to eat her truffles. Given that each truffle has a radius of 0.
The surface area of a circular cone can be calculated by summing the surface area of each of its individual components. The "base SA" refers to the circle that comprises the base in a closed circular cone, while the lateral SA refers to the rest of the area of the cone between the base and its apex. The equations to calculate each, as well as the total SA of a closed circular cone are shown below:.
Athena has recently taken an interest in Southeast Asian culture, and is particularly fascinated by the conical hat, typically referred to as a "rice hat," which is commonly used in a number of southeast Asian countries.
She decides to make one of her own, and being a very practical person not mired in sentimentality, retrieves her mother's wedding dress from the dark recesses of the wardrobe in which it resides.
She determines the surface area of material she needs to create her hat with a radius of 1 foot and a height of 0.
Anne wants to give her younger brother a Rubik's cube for his birthday, but knows that her brother has a short attention span and is easily frustrated.
She custom orders a Rubik's Cube in which all the faces are black, and has to pay for the customization based on the surface area of the cube with an edge length of 4 inches. The surface area of a closed cylinder can be calculated by summing the total areas of its base and lateral surface:.
Jeremy has a large cylindrical fish tank that he bathes in because he doesn't like showers or bathtubs. He is curious whether his heated water cools faster than when in a bathtub, and needs to calculate the surface area of his cylindrical tank of height 5.
The total area occupied by the surfaces of an object is called its surface area. The surface area is classified into two categories:. The area of the whole of anything, whether it's an object or a surface, is the sum of the area of its constituent parts. We now know that the surface area of a three-dimensional object is the total area of all of its surfaces.
In this section, we will learn about the various formulas used to calculate the surface area of different objects. The surface area of the cube is the total area covered by all six faces of the cube.
The general formula of the surface area of a cube is given as:. The total surface area of the cube will be the sum of the area of the base and the area of vertical surfaces of the cube.
There are 4 side faces so the sum of areas of all 4 side faces of a cube is its lateral area. The surface area of cuboid can be explained in terms of two different categories of area, i.
The total surface area of the cuboid is obtained by adding the area of all the 6 faces whereas the lateral surface area of the cuboid is found by finding the area of each face excluding the base and the top. The total surface area and lateral surface area can be expressed in terms of length l , breadth b , and height of cuboid h as:. The surface area of a cone is the amount of area occupied by the surface of a cone. A cone is a 3-D shape that has a circular base.
This means the base is made up of a radius and diameter. As a cone has a curved surface, thus we can express its curved surface area as well as total surface area. When it comes to knowing the volume and surface area of these objects, there are two definitions that you have to know. Surface area is the area of all outer facing surfaces on an object. The total surface area is calculated by adding all the areas on the surface: the areas of the base, top, and lateral surfaces sides of the object.
This is done using different area formulas and measured in square units. Volume is the amount of space that a three dimensional object takes up.
These equations will give you correct answers if you keep the units straight. All rights reserved. Legal Notices. Please read our Privacy Policy. Email this page to a friend. Surface Area Formulas.
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