Category: 05. Volume and surface area of shapes

Here, we provide you with volume formulas for some common three-dimensional figures and also for the ellipsoid and the hollow cylinder that are not so common. Cube: Volume = a3 = a × a × a Cylinder: Volume = π × r2 × h π = 3.14h is the heightr is the radius Rectangular solid or cuboid:…

Understanding volume or capacity is especially important in the field of medicine or chemistry when one is dealing constantly with liquid measurement. What is volume or capacity? Although volume and capacity are very similar, there is a tiny difference. In math, capacity is the amount a container will hold when full while volume refers to…

The volume of a pyramid is how much space the pyramid occupies. We will start with a pyramid that has a square as the base. Look carefully at the pyramid shown below to see how the volume can be computed. Volume of a pyramid formula Suppose B is the area of the base, h is…

Given the radius or r and the height or h, the volume of a cone can be found by using the formula: Formula: Vcone = 1/3 × b × h b is the area of the base of the cone. Since the base is a circle, area of the base = π × r2 Thus, the…

Given the radius or r and height or h, the volume of cylinders can be found by using the formula: Volume of a cylinder = area of base × height = π × r2× h and you can use 3.14 for π. Notice that the base of the cylinder is a circle and the formula…

When the three radii are known, the volume of an ellipsoid can be calculated by using the formula you see below: The formula can also be written as V =  4 × π × a × b × c3Use π = 3.14 Some examples showing how to find the volume of an ellipsoid. Example #1…

The volume of a sphere is how much space the sphere occupies. In the figure below, notice that the sphere on the left occupies less space than the sphere on the right. Therefore, the sphere on the left has less volume.  Volume of a sphere formula Given the radius, the volume can be found by using…

Given the length, the height, and the width, the volume of a box also called rectangular prism can be found by using the following formula in the figure below. It is not always straightforward to label the height, the width, and the length. It is just a matter of perspective! Looking at the box below,…

The volume of a cube is how much space the cube occupies. Given the length of one side, call it a, the volume of any cube can be found by using the following formula: Volume of a cube formula Volume of any cube = a3 = a × a × a If a is the edge…

How to calculate the volume of solids, such as the cube, the sphere, the cylinder, the pyramid, the cone, the ellipsoid, and the rectangular prism is what you will learn here.  As a warm up, take a look at the figure below looking like a pencil. How would you calculate the volume of the pencil…