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Calculating the Area and Volume of a Right Circular Cone

volume of a right circular cone: cone

Let’s get right to it — we’re here to calculate the surface area or volume of a right circular cone. As you might already know, in a right circular cone, the height goes from the cone’s vertex through the center of the circular base to form a right angle. Right circular cones are what we typically think of when we think of cones.

There are two right circular cone formulas to know: The formula for the volume of a cone is (𝛑r²h)/3. The formula for the surface area of a right circular cone is 𝛑rs+𝛑r². Let's look at them both in further detail.

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How to Find the Volume of a Half Sphere

how to find volume of half sphere: 3D sphere in half

Understanding how to find the volume of a half sphere, or in other words, the volume of a hemisphere, is easier than it seems. Keep in mind that volume is the amount of space that a three-dimensional shape takes up, whereas the surface area is the total area of all the surfaces of that three-dimensional shape.

First, we need to review the formula for the volume of the sphere. The volume formula for a sphere is (4𝛑r²)/3, where r stands for the radius of the sphere. (The radius is the distance from the center of the sphere).

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How to Find Volume and Surface Area for 6 Common Shapes

volume and surface area: Chart of different shapes and areas with formulas

Our world is filled with three-dimensional objects. When it comes to knowing the volume and surface area of these objects, there are two definitions that you have to know. Surface area is the area of all outer facing surfaces on an object. The total surface area is calculated by adding all the areas on the surface: the areas of the base, top, and lateral surfaces (sides) of the object. This is done using different area formulas and measured in square units.

Volume is the amount of space that a three dimensional object takes up. There are also different formulas for different three-dimensional shapes. The total volume of an object is measured in cubic units.

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Learning and Solving Systems of Equations Word Problems

systems of equations word problems: Person writing a mathematical equation on a blackboard

When it comes to solving systems of equations word problems, don't forget that they're not just problems that will show up on your Common Core State Standards (CCSS) worksheets and test prep. They are often real-world problems with many applications.

A system of equations is just a fancy name for a problem with multiple equations. Often, the first equation is primary and the second equation helps you solve for the first equation.

In this article, we'll take you through an example that shows how the substitution method in systems of linear equations can help solve for both of the original equations.

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Your Guide to Understanding and Using Powers of 10

powers of 10: Box of beads, number cards and letter cutouts on a wooden surface

Our number system is based on powers of ten, meaning that moving the decimal point right or left one digit changes the original number by a magnitude of 10. For example, 0.1 is 10 times smaller than 1. 100 is 10 times bigger than 10.

Each zero that we add moves the 1 over another place value from the ones digit to the tens digit to the hundreds digit to the thousands digit. We know that as the decimal place moves to the left of zero, we go from the tenths digit to the hundredths digit to the thousandth digit and so on.

Let's look more closely at ways to work with powers of 10.

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