3.5 Volume and Surface Area

Volume and Surface Area
3.5

Apply the relationship between the volume and surface area formulas for cylinders, spheres, and cones to solve real world problems.

Volume

We measure the volume of a three-dimensional figure using cubic units. Volume Equals Area of Base Times Height

If an object has a flat top and base and sides perpendicular to the base, as shown, then, if the area of the base is A and the height is h, the volume will be V = A · h.

Surface Area

Surface Area is the total area of the faces of a three-dimensional shape. It's the amount of space that the surface of an object takes up.

-Measured in square units

*Surface Area is different from volume, which is the amount of space available in an object. Surface area is used in real life when we want to wrap something, paint, or build things.

Prism

Volume and Surface Area of a Right Circular Cylinder

A right circular cylinder with radius r and height h has volume
V = πr²h and
surface area

S = 2πrh + 2πr².​

Cylinders

Cones

Sphere