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. Where r is the radius and h is the heightĪthena 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. The equations to calculate each, as well as the total SA of a closed circular cone are shown below: 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 surface area of a circular cone can be calculated by summing the surface area of each of its individual components. Given that each truffle has a radius of 0.325 inches: 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. Xael doesn't like sharing her chocolate truffles with anyone. The surface area (SA) of a sphere can be calculated using the equation: Please refer to the aforementioned calculators for more detail on each individual object. As such, this calculator will focus on the equations for calculating the surface area of the objects and the use of these equations. All of the objects addressed in this calculator are described in more detail on the Volume Calculator and Area Calculator pages. The surface area of a solid is a measure of the total area occupied by the surface of an object. Related Volume Calculator | Area Calculator | Body Surface Area Calculator Square Pyramid Surface Area Base Edge (a) Base Radius (r)Ĭonical Frustum Surface Area Top Radius (r) Please provide any two values below to calculate. Ball Surface Area Radius (r)Ĭylindrical Tank Surface Area Base Radius (r) Use the calculators below to calculate the surface area of several common shapes. Therefore, the surface area of the square prism is 432 cm^2 and the volume is 324 cm^3.Home / math / surface area calculator Surface Area Calculator Volume of Prism = Area of Base x Height = (36 cm^2)(9 cm) = 324 cm^3 Surface Area of Prism = 2 x Area of Base + Perimeter of Base x Height = 2(36 cm^2) + (24 cm)(9 cm) = 432 cm^2 Perimeter of Base = 4 x side = 4 x 6 cm = 24 cm Example 3: Square Prismįind the surface area and volume of a square prism with side length = 6 cm and height = 9 cm.Īrea of Base = side x side = 6 cm x 6 cm = 36 cm^2 Therefore, the surface area of the triangular prism is 304 cm^2 and the volume is 240 cm^3. Volume of Prism = Area of Base x Height = (30 cm^2)(8 cm) = 240 cm^3 Surface Area of Prism = 2 x Area of Base + Perimeter of Base x Height = 2(30 cm^2) + (32 cm)(8 cm) = 304 cm^2 Perimeter of Base = sum of lengths of sides of triangle = 10 cm + 10 cm + 12 cm = 32 cm Example 2: Triangular Prismįind the surface area and volume of a triangular prism with base = 10 cm, height of base = 6 cm, and height of prism = 8 cm.Īrea of Base = 1/2 x base x height of base = 1/2 (10 cm) (6 cm) = 30 cm^2 Therefore, the surface area of the rectangular prism is 192 cm^2 and the volume is 120 cm^3. Volume of Prism = Area of Base x Height = (20 cm^2)(6 cm) = 120 cm^3 Surface Area of Prism = 2 x Area of Base + Perimeter of Base x Height = 2(20 cm^2) + (18 cm)(6 cm) = 192 cm^2 Perimeter of Base = 2(length + width) = 2(5 cm + 4 cm) = 18 cm Solve Examples: Example 1: Rectangular Prismįind the surface area and volume of a rectangular prism with length = 5 cm, width = 4 cm, and height = 6 cm.Īrea of Base = length x width = 5 cm x 4 cm = 20 cm^2 By understanding the formula for calculating the area of a prism and its types, you can apply this knowledge to various fields such as architecture, optics, and packaging. The area of a prism is an important concept in geometry that has many real-world applications. It is called a cylinder, and the formula for calculating its area is different from that of other prisms. Yes, you can have a prism with a circular base. Can you have a prism with a circular base? What is the difference between a rectangular prism and a cube?Ī cube is a type of rectangular prism where all the sides are equal in length. To find the volume, you need to use a different formula. No, the formula for calculating the area of a prism only gives you the surface area of the shape. Packaging: Prisms are used in packaging to create unique and appealing shapes and designs.įAQs: Can you use the formula for the area of a prism to find the volume?.Optics: Prisms are used in optical devices such as binoculars, cameras, and telescopes to bend and manipulate light.Architecture: Prisms are commonly used in architecture, especially in the construction of buildings and bridges.
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