Scientific Calculator

A calculator is a device that performs arithmetic operations on numbers. The simplest calculators can do only addition, subtraction, multiplication, and division. More sophisticated calculators can handle exponential operations, roots, logarithm s, trigonometric functions, and hyperbolic functions.

The surface area of a solid is a measure of the total area occupied by the surface of an object. All of the objects addressed in this calculator are described in more detail on the Volume Calculator and Area Calculator pages. As such, this calculator will focus on the equations for calculating surface area the objects and the use of these equations. Please refer to the aforementioned calculators for more detail on each individual object.

Sphere

The surface area (SA) of a sphere can be calculated using the equation:

SA = 4πr2

where r is the radius

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 0.325 inches:

SA = 4 × π × 0.3252 = 1.327 in2

Cone

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:

base SA = πr2

lateral SA = πr√r2 + h2

total SA = πr(r + √r2 + h2)

where r is radius and h is height

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 0.5 feet as follows:

lateral SA = π × 0.4√0.42 + 0.52 = 0.805 ft2

Cube

The surface area of a cube can be calculated by summing the total areas of its six square faces:

SA = 6a2

where a is edge length

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 edge length of 4 inches.

SA = 6 × 42 = 96 in2

Cylindrical Tank

The surface area of a closed cylinder can be calculated by summing the total areas of its base and lateral surface:

base SA = 2πr2

lateral SA = 2πrh

total SA = 2πr(r + h) where r is radius and h is height

Jeremy has a large cylindrical fish tank that he bathes in because he doesn't like showers or bath tubs. 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 5.5 feet and radius of 3.5 feet.

total SA = 2π × 3.5(3.5 + 5.5) = 197.920 ft2

Rectangular Tank

The surface area of a rectangular tank is the sum of the area of each of its faces:

SA = 2lw + 2lh + 2wh

where l is length, w is width, and h is height