lateral SA = πr√r2 + h2 The surface area formula for a triangular prism is 2 * (height x base / 2) + length x width1 + length x width2 + length x base, as seen in the figure below: A triangular prism is a stack of triangles, so the usualy triangle solving rules apply when calculating the area of the bases. The equations to calculate each, as well as the total SA of a closed circular cone are shown below: base SA = πr2 where a, b, and c are the axes of the ellipse. Rectangular prism is a solid three dimensional object, it has either six flat surfaces of rectangles or four rectangles with two squares. The surface area of a capsule can be determined by combining the surface area equations for a sphere and the lateral surface area of a cylinder. Below are the standard formulas for surface area. The surface area of a rectangular prism formula is. Use the calculators below to calculate the surface area of several common shapes. Body Surface Area Calculator. All rights reserved. Total Surface Area = L + B = a 2 + a√(a 2 + 4h 2)) = a(a + √(a 2 + 4h 2)) Rectangular Prism Surface Area Volume = lwh; Surface Area = 2(lw + lh + wh) Sphere Surface Area Volume = (4/3) π r 3; Surface Area = 4 π r 2; Spherical Cap Surface Area The surface area of a solid is a measure of the total area occupied by the surface of an object. The surface area of a closed cylinder can be calculated by summing the total areas of its base and lateral surface: base SA = 2πr2 h = height where R and r are radii of the ends, h is height. Given that each truffle has a radius of 0.325 inches: The surface area of a circular cone can be calculated by summing the surface area of each of its individual components. total SA = 2πr(r + h) Total solid sphere SA = 2πRh + πr2 Please provide any two values below to calculate. Given two values of height, cap radius, or base radius, the third value can be calculated using the equations provided on the Volume Calculator. Although his volcano is unlikely to impress the science fair judges, Paul must still determine the surface area of material he needs to coat the outer wall of his volcano with R of 1 foot, r of 0.3 feet, and h of 1.5 feet: total SA = π(12 + 0.32) + π(1 + 0.3) √(1 - 0.3)2 + 1.52 = 10.185 ft2. She calculates the surface area of melted sugar she would need to fully coat the pyramid with edge length a of 3 feet and height h of 5 feet: total SA = 32 + 2 × 3√(3/2)2 + 52 = 40.321 ft2. Rather than eating his vegetables, Coltaine's father stares dejectedly at his plate, and estimates the surface area of the elliptical cuts of zucchini with axes 0.1, 0.2, and 0.35 inches: SA ≈ 4π 1.6√( + + = 0.562 in2. The surface area equations are as follows: spherical cap SA = 2πRh where r is radius and h is height. Since Jennifer is two-thirds the age of her brother, she decides that she deserves one-third of her brother's globe. The surface area (SA) of a sphere can be calculated using the equation: Xael doesn't like sharing her chocolate truffles with anyone. If you'd like to cite this online calculator resource and information as provided on the page, you can use the following citation: Georgiev G.Z., "Surface Area Calculator", [online] Available at: URL [Accessed Date: 13 Nov, 2020]. total SA = π(R2 + r2) + π(R+r)√(R-r)2 + h2 SA=2 (lw+hw+lh), where. Unfortunately for his family, who almost exclusively eat meat, Coltaine has been practicing his cutting technique on an excessive amount of vegetables. 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. Paul views volcanic eruptions as a violent phenomenon, and being against all forms of violence, decides to make his volcano in the form of a closed conical frustum that does not erupt. Our online calculators, converters, randomizers, and content are provided "as is", free of charge, and without any warranty or guarantee. However, she feels that the model does not exude the feeling of architectural wonder that the original does and decides that coating it with "snow" would at least impart an aspect of wonder. The surface area formula for a cone, given its diameter (or radius) and height is π x (diameter / 2)2 + π x (diameter / 2) x √ ((diameter / 2)2 + (height2)), where (diameter / 2) is the radius of the base (d = 2 x r), so another way to write it is π x radius2 + π x radius x √ (radius2 + (height2)), as seen in the figure below: The surface area of a cone is one of the most complicated and it is where the need for a calculator becomes more apparent. total surface area). This surface area of a sphere calculator below is very simple to use. where R is spherical cap radius, r is base radius, and h is height. The surface area of a spherical cap is based on the height of the segment in question. In all surface area calculations, make sure that all lengths are measured in the same unit, e.g. The total surface area is calculated as follows: SA = 4πr2 + 2πrh where r is radius and h is height. 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 rectangular tank is the sum of the area of each of its faces: SA = 2lw + 2lh + 2wh Horatio is manufacturing a placebo that purports to hone a person's individuality, critical thinking, and ability to objectively and logically approach different situations. Units: Note that units are shown for convenience but do not affect the calculations.