Volume of a Pyramid
The formula for calculating the volume of a pyramid is:
where B is the area of the base and h is the height. Try to find the volume of the pyramid below:
The base is just a square with a side of
3, and the height is
3
/2.
B = 32 = 9, and the total volume of the pyramid is:
Surface Area of a Pyramid
The surface area of a pyramid is rarely tested on the Math IC test. If you come across one of those rare questions that covers the topic, you can calculate the area of each face individually using techniques from plane geometry, since the base of a pyramid is a square and the sides are triangles. Practice by finding the surface area of the same pyramid in the figure below:
To calculate the surface area, you need to add together the area of the base and the areas of the four sides. The base is simply a square, and we’ve seen that B = 32 = 9. Each side is an equilateral triangle, and we can use the properties of a 30-60-90 triangle to find their areas:
Spheres
A sphere is the collection of points in three-dimensional space that are equidistant from a fixed point, the center of the sphere. Essentially, a sphere is a 3-D circle. The main measurement of a sphere is its radius, r, the distance from the center to any point on the sphere.
If you know the radius of a sphere you can find both its volume and surface area. The equation for the volume of a sphere is:
The equation for the surface area of a sphere is:
3 
/2
/ 4
/4
