Learning Volume

Tutorials, Tips, and Sample Problems

What is Volume?

Volume is the amount of space, in cubic units, that occupies a three dementional figure. The shapes that you can find the volumes of are prisms, pyramids, cones, cylinders, and spheres. Prisms and pyramids differ based on the shapes of their bases.

Volume of a Rectangular Prism

The equation for the volume of a rectangular prism is V=Bh.

First, you would need to find the area of the base, or B. To do so, you would multiply the length and the width of the base. You would then multiply that by the height of the prism, or h. That process would give you the volume of a rectangular prism.

Volume of a Triangular Prism

The equation for the volume of a triangular prism is V=Bh. It has a twist though. The base is a different shape, changing the process slightly.

First, you find the area of the base, or B. To do so, you must multiple the base, and the height of the triangle. Then divide that by 2. You would then have to multiply that answer with the height of the prism, or h. That process will give you the volume of a triangular prism.

Volume of a Square Pyramid

The equation for the volume of a square pyramid is V=1/3Bh.

To do this you need to find area of the base, or B. You will multiply the base of the square, and the height of the square. Then multiple that answer with the height of the pyramid or h. After you find that, you need to multiple it by 1, the numerator, and divide it by 3, the denominator. In other words, since the numerator is one and the answer multiplied by 1 would stay the same, you can omit, or delete that step and just divide by 3. This gets you the volume of a square pyramid.

Volume of a Triangular Pyramid

The equation for the volume of a triangular pyramid is V=1/3Bh. Again, the base is different, causing the process to change slightly.

To do this, you need to find the area of the base, or B. You would multiple the base of the triangle, by the height of the triangle. Take that answer and divide it by 2. Then, multiple that answer by the height of the whole pyramid, or h. After that, multiply it by 1, the numerator, and divide it by 3, the denominator. Again, multiplying by 1 is useless because the answer wouldn't change, so you only need to divide by 3. This gives you the volume of a triangular pyramid.

Volume of a Sphere

The equation for the volume of a sphere is 4/3π(r)(r)(r).

You will need multiple the radius of the sphere to the power of 3, and then multiply that by Pi, or 3.14 to get the area of the inner circle. Then multiply that answer by 4, the numerator, and divide it by 3, the denominator. This gives you the volume of a sphere.

Volume of a Cylinder

The equation for the volume of a cylinder is V=Bh.

To find the area of the base, or B, you need to multiply the radius of the circle to the power of 2, and then multiply that by Pi, or 3.14. Then multiply that by the height of the cylinder, or h. This gives you the volume of a cylinder.


Volume of a Cone

The equation for the volume of a cone is V=1/3Bh.

You need to find the area of the base, or B. To do so, you need to multiply the radius of the circle to the power of 2 and then multiply that by Pi, or 3.14. Then multiply that by the height of the cone, or h. Take that and multiply it by 1, the numerator, and divide it by 3, the denominator. Again, multiplying by 1 is useless, so you only have to divide by the denominator.

Falisha's Dollhouse

Falisha has a square pyramid a base of 49 square centimeters and a height of 24 centimeters stacked on a rectangular prism with the dimensions of 7, 7, and 6 to make a dollhouse. What is the total volume of the dollhouse?


You would find the volume of the rectangular prism, V=Bh, or V= (7)(7)(6). Then you would find the volume of the square pyramid, V=1/3Bh, or V=1/3(49)24. You would then add them together to get the total volume.