Surface Area Formula | How to Find Surface Area – Video & Lesson Transcript | https://epicentreconcerts.org

What is Surface Area

The surface area measures the area of the outside of a three-dimensional shape. It can be described as the space covering the outdoor of a solid calculate. Surface area and area are both measured in square units, but they are not the lapp. For example, the sphere of a compressed, planar word picture is the space covered by the paper. This paint is on the page of a magazine. The page is flat, with just two dimensions : distance and width.

page of magazine with picture of flowers

contrast that with the coat area of a painted box. The box is a three-dimensional aim and has three dimensions : length, width, and depth .

painted box

just like there are formulas for calculating the area of a planar shape, there are formulas for calculating the surface area of a cubic solid .

Calculating Surface Area

How can a person find the surface area of a firm form ? One way to think of calculating come on area is to find the sum of the individual areas of each side. There are besides rule for calculating the surface area of different cubic objects. Different solid shapes have different formulas. respective examples of hearty shapes and the recipe for calculating their surface area can be found here .

Surface Area of a Sphere

A ball is an model of a sphere, a cubic object. How is the surface area of a sphere calculated ? There is a formula for the surface area of a sphere. here is an example of using the formula to find the surface area of a sphere. Recall the basketball at the get down of the lesson. The surface area of the basketball, a sphere, measures the sum of leather covering the outside of the ball. The formula for the coat area of a sphere requires knowing the sphere ‘s radius. The radius of the basketball is 5 inches .

basketball diagram

The surface area recipe for a sphere is : { equivalent } SA=4 \pi r^2 { /eq } Use a radius of 5 inches. { equivalent } SA=4 \pi 5^2 { /eq } { equivalent } SA \approx 314.2 { /eq } The airfoil area of the basketball, which is the come of leather covering the external of the basketball, is approximately 314.2 square inches .

Surface Area of a Cone

A traffic cone is an case of a cone, a three-dimensional object. How is the coat area of a cone calculated ? There is a rule for the come on area of a cone. here is an exemplar of using the rule to find the surface sphere of a cone. Think about the traffic cone. The surface sphere of the dealings cone measures the amount of formative covering the away of the cone, including its round root. The rule for the airfoil area of a cone requires knowing the radius of the round base and the cant height of the cone. The spoke of the cone ‘s nucleotide is 5 inches. The pitch acme of the cone is 20 inches .

cone with labeled slant height

The surface area formula for a cone is : { equivalent } SA = \pi r^2 + \pi radius south { /eq } Use the radius of 5 inches and the slant height of 20 inches. { equivalent } SA = \pi 5^2 + \pi ( 5 ) ( 20 ) { /eq } { equivalent } SA \approx 78.5 + 314.2 { /eq } { equivalent } SA \approx 392.7 { /eq } The surface area of the cone, which is the sum of plastic covering the outside of the cone, including the cycle base, is approximately 392.7 square inches .

Surface Area of a Cube

A child ‘s wooden ABC block is an example of a cube, a cubic object. How is the surface area of a cube calculated ? There is a rule for the come on sphere of a cube. here is an example of using the formula to find the surface area of a cube. Think about the child ‘s wooden ABC auction block. The surface area of the jam, a cube, measures the come of paint need to cover the outside of the block. The formula for the surface area of a block requires knowing the length of one side, or edge, of the cube. Remember, all sides of a cube are the like distance. The distance of one side of the child ‘s ABC engine block is 3 centimeters .

3 cm labeled cube

The surface sphere formula for a cube is : { equivalent } SA = 6 s^2 { /eq } Use the side length of 3 centimeters. { equivalent } SA = 6 ( 3^2 ) { /eq } { equivalent } SA = 54 { /eq } The surface area of the child ‘s ABC block, which is the total of key needed to cover the outside of the barricade, is 54 hearty centimeters .

Surface Area of a Cylinder

A can is an exercise of a cylinder, a cubic object. How is the airfoil area of a cylinder calculated ? There is a convention for the surface sphere of a cylinder.

here is an model of using the rule to find the surface area of a cylinder. Think about the can. The surface sphere of the can, a cylinder, measures the measure of metallic covering the outside of the can. The recipe for the surface sphere of a cylinder requires knowing the radius of the circular root of the can and the can ‘s acme. The spoke of the circular al-qaeda of the can is 1.5 inches, and the can ‘s stature is 7 inches .

labeled cylinder

The surface area recipe for a cylinder is : { equivalent } SA=2 \pi rh + 2 \pi r^2 { /eq } Use the radius of 1.5 inches and the altitude of 7 inches. { equivalent } SA=2 \pi ( 1.5 ) ( 7 ) + 2 \pi ( 1.5^2 ) { /eq } { equivalent } SA \approx 66.0 + 14.1 { /eq } { equivalent } SA \approx 80.1 { /eq }
The airfoil area of the can, which is the amount of metallic element covering the external of the can, is approximately 80.1 square inches .

Surface Area of a Rectangular Prism

A cereal box is an case of a orthogonal prism, a cubic object. How is the come on sphere of a rectangular prism calculated ? There is a convention for the surface area of a rectangular prism. here is an exemplar of using the formula to find the surface area of a orthogonal prism. Think about the cereal box. The surface area of the grain corner, a orthogonal prism, measures the come of cardboard covering the outside of the box. The rule for the airfoil area of a rectangular prism requires knowing the length, width, and altitude of the prism. The cereal box is 8 inches long, 2 inches wide, and 12 inches tall .

labeled rectangular prism

The come on area convention for a rectangular prism is : { equivalent } SA=2 ( lw + wh + hectoliter ) { /eq } Use the length of 8 inches, width of 2 inches, and stature of 12 inches. { equivalent } SA=2 ( ( 8 ) ( 2 ) + ( 2 ) ( 12 ) + ( 12 ) ( 8 ) ) { /eq } { equivalent } SA = 2 ( 16 + 24 + 96 ) { /eq } { equivalent } SA = 2 ( 136 ) { /eq } { equivalent } SA = 272 { /eq } The surface area of the cereal box, which is the measure of cardboard covering the external of the box, is 272 squarely inches. Another way to find the surface area of a rectangular prism is to find the perimeter of the base and breed by the height, then add the area of the bases. SA = ( margin of nucleotide ) ( height ) + ( area of bases ) SA = ( 8 + 2 + 8 + 2 ) ( 12 ) + ( 2 ) ( 2 ) ( 8 ) SA = 240 + 32 = 272 This method acting results in the same surface area of 272 square inches .

Surface Area of a Square-Based Pyramid

A tent with a square floor is an case of a square-based pyramid, a three-dimensional object. How is the surface area of a square-based pyramid calculated ? There is a formula for the surface area of a square-based pyramid. hera is an exemplar of using the rule to find the surface area of a square-based pyramid. Think about the tent with the square floor. The coat area of the tent, a square-based pyramid, measures the sum of fabric covering the outside of the camp, including the floor. The rule for the surface area of a square-based pyramid requires knowing the length of one side of the tent ‘s square floor and the slant altitude of the camp. The square floor of the camp is 6 feet long on each side, and the slant stature of the tent is 7.5 feet .

labeled pyramid

The open area formula for a square-based pyramid is : { equivalent } SA=2 ( l ) ( second ) + l^2 { /eq } Use the side distance of 6 feet and the slant acme of 7.5 feet. { equivalent } SA=2 ( 6 ) ( 7.5 ) + 6^2 { /eq } { equivalent } SA=90+36 { /eq } { equivalent } SA = 126 { /eq }

The surface sphere of the tent, which is the amount of fabric covering the outside of the tent, including the floor, is 126 square feet .

Lesson Summary

What is coat area ?

  • Surface area measures the space needed to cover the outside of a three-dimensional shape.
  • Surface area is the sum of the areas of the individual sides of a solid shape.
  • Surface area is measured in square units.
  • There are formulas to find the surface area of different solid shapes.

Formulas for how to find surface sphere :

  • sphere {eq}SA=4 \pi r^2 {/eq} where r = radius of sphere
  • cone {eq}SA = \pi r^2 + \pi r s {/eq} where r = radius of sphere and s = slant height of cone
  • cube {eq}SA = 6 s^2 {/eq} where s = length of one side of cube
  • cylinder {eq}SA=2 \pi rh + 2 \pi r^2 {/eq} where r = radius of circular base and h = height of cylinder
  • rectangular prism {eq}SA=2(lw + wh + hl) {/eq} where l = length, w = width, and h = height of prism OR SA = (perimeter of base)(height) + (area of bases)
  • square-based pyramid {eq}SA=2(l)(s) + l^2 {/eq} where l = length of one side of base and s = slant height of pyramid

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