Surface Area Introduction

Surface Area

-OR- How much space is ON the thing?

​What is Surface Area?

Surface area is the amount of space covering the outside of a three-dimensional shape. For example, your surface area would essentially be your skin and how much area it takes up. In Geometry, we will be looking at the Surface Area of our fundamental 3D shapes. First, let's name them.

Prisms are unique in that the formula changes depending on what the BASE of the prism is. We also name our prisms this way. For example, if the base of the prism is a pentagon, then we call it a Pentagonal Prism. Cubes are a special prism, in that all 6 faces are exactly the same square.

Prisms are 3D shapes that are connected by two similar polygons. For our purposes, we will be sticking with Right Prisms, meaning the two bases will be congruent and will not have a slant.

Prisms

Match

Match the image of the 3D shape with its name.

Prism

Pyramid

Cylinder

Cone

Sphere

• Prism

• Pyramid

• Cylinder

• Cone

• Sphere

Pyramids follow a similar rule, in that the formula changes by what the BASE shape is. This also changes the name. For example, if the bottom of the pyramid is a square, we call it a Square Pyramid.

Pyramids are 3D shapes that have one polygonal base that connects to an apex (point at the top).

Pyramids

Circles are not polygons and thus have different shapes on their own.

​
Cylinders are two circles as the bases, which are then connected. We will be using Right Cylinders, so there is no slant.

Cones have a base that is a circle that connects up to an apex. That's what we put ice cream in.

Spheres are... well, balls.

The Circle Ones

Math Response

Now, let's practice finding the total surface area of various 3D shapes. We will start with a cube. Envision a cube in your minds eye. If the length of one of the edges of the cube is 3 units, how many units is the total surface area?

Type answer here

Correct Answer: 54

Deg^°

Rad

Math Response

Now image a rectangular prism. The length is 2 units, the width is 3 units and the height is 4 units. What is the total surface area?

Type answer here

Correct Answer: 52

Deg^°

Rad

Math Response

Now imagine a cone. The radius is 3 units and the height is 4 units. What is the total surface area? (HINT: This is kind of a trick question. Really pay attention to the equation)

Round to one decimal place.

Type answer here

Correct Answer: 75.4

Deg^°

Rad

Math Response

Now, let's do a cylinder. The diameter of the cylinder is 8 units, and the height is 10 units. What is the total surface area? Leave your answer in terms of pi.

NOTE: That means, do not actually use pi. Your answer should have pi in it.

Type answer here

Correct Answer: 112\pi

Deg^°

Rad

Math Response

Now I have a ball with a radius of 4 units. What is the total surface area? Leave in terms of pi.

Type answer here

Correct Answer: 64\pi

Deg^°

Rad

Math Response

Last one. Now I have a triangular prisms. The triangle is an equilateral triangle. The base of the triangle is 10 and the height is 4. The length of the prisms is 20. What is the total surface area?

HINT: Really analyze the picture and the language of the question.

Type answer here

Correct Answer: 640

Deg^°

Rad

Really Pay Attention

The language might be tricky sometimes, or the labeling on the shape might be a little different than what is expected. You need to pay attention to what it is you are looking at. If you do, you'll be able to solve any of these problems with ease. It's all multiplication and addition- just make sure you put the right numbers in the right place.