What is Surface Area?
Concept
The surface area of a three-dimensional object is the total area of all of its surfaces. 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.
Rules
Method 1:
Look at the pattern obtained when a three-dimensional figure is laid out flat showing each face of the figure. To find the total area of the net, calculate the area of each separate shape and add the areas together.
Method 2:
1. Use formulae to calculate the surface area of different 3D solids.
2. Substitute the measurements given into the required formula.
3. Use order of operations to solve to find the surface area.
i. Use the formula 6a2 to find the the surface area of a cube, where a is the side length of the cube.
ii. Use the formula b x h to find the the surface area of a prism, where b is the base area and h is the height of the prism.
iii. Use the formula S.A. = 2πrh + 2πr2 to find the the surface area of a cylinder, where r is the radius and h is the height of the cylinder.
iv. Use the formula S.A. = πrl + πr2 to find the the surface area of a cone, where r is the radius and l is the slant height of the cone.
v. Use the formula S.A. = to find the the surface area of a pyramid, where B is the area of the base, P is the perimeter of the base and l is the slant height of the pyramid.
Example
What is the surface area of the rectangular prism?
Solution
Surface Area = 2lw + 2lh + 2hw
= 2(6 cm x 10 cm) + 2 (6 cm x 4 cm) + 2 (4 cm x 10 cm)
= 120 cm2 + 48 cm2 + 80 cm2
= 248 cm2
Practice What is Surface Area
Practice Problem 1
Find the surface area.
Practice Problem 2
Find the total surface area of the pyramid.
Practice Problem 3
Calculate the surface area of the cone shown below.
Round to the nearest tenth. Use 3.14 for π.
Practice Problem 4
Find the surface area of the composite figure.
Area – The space occupied by a flat shape or the surface of an object. The area of a figure is the number of unit squares that cover the surface of a closed figure.
Surface area is the sum of the areas of all faces (or surfaces) on a 3D shape.
A three-dimensional shape is a solid shape that has height and depth.
A rectangular prism is a solid (3-dimensional) object which has six faces that are rectangles.
Regular pyramid – a pyramid with a base that is a regular polygon.
Cylinder – A three-dimension figure with two parallel congruent circular bases connected by a curved surface.
Cone – A three-dimensional figure with one circular base connected by a curved surface to a single vertex.
Lateral surface area – the sum of all of the lateral faces.
Slant height – the height of a lateral face.