I have always wondered about this question: How do you derive the volumes of shapes? Why is the volume of a square based pyramid 1/3b^2(h)?? Why is the volume of a sphere 4/3(pi)r^3? Actually, in order to prove that these are the volumes of the sphere and square based pyramid, we have to use calculus. Calculus? Yup. In order to prove that 4/3(pi)r^3 is the volume of a sphere, you have to use integrals and basic knowledge of volumes. If you do not know what integrals are, that's okay! Watch out for my future blog posts on integrals! First, you have to find the cross-sectional volume of the shape. For instance, if the shape was a sphere, you find the cross-sectional volume of the 'disc' inside the sphere. This allows you to find one portion of the volume. You then integrate the prticular volume to a certain limit (of the 3d whole shape). Good luck,
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Engineering. What is it? Being a daughter of two people who chose a technical field, this word has been in the 'most heard words' list throughout my life so far. People usually infer Engineering to involve buildings, architecture, and construction. And I don't blame them. I always used to think that engineering is just something that has to do with building structures. If you think that my friend, your interpretation is slightly wrong. Lets take a close look at what Engineering really is:
Engineering is a field of studies which incorporates fundamentals of mathematics and science, and can be used to solve real world problems around the world. Yes, this is Engineering. From the smallest particles of the universe to the largest solar panels, engineering can be used to modify anything in order for it to be more efficient and effective. More efficient and effective things can help people in this world!! That is why it is considered and regarded as a broad field. For instance, you can decide to take Biomedical Engineering, a type of engineering which is all about designing medical technological systems for others. There are many other specializations of Engineering. Comment down which one is yours! On top of that, Engineering involves creativity and minds which think differently. Companies like Apple, or Google require many engineers in order to process multiple ideas and bring them to life. Good luck, Have you wondered the same thing? I was learning about SA and Volume of 3 dimensional composite shapes at school when I thought, 'Why is the Surface Area of a Sphere 4(pi)r^2?' How did mathematicians derive this formula? Why does this formula make sense? There is actually a simple mathematic logic for the derivation of this particular formula. The formula was first found by Archimedes (my mathematician buddy). Archimedes proved that the surface area of a sphere is equal to the lateral surface area of a cylinder. The lateral surface area of a cylinder does not include the area of the two circular ends. For a sphere to nicely fit inside a cylinder, the height of the cylinder should be twice the sphere's radius, 2r. If the height of the cylinder is 2r, then its lateral surface area is: circumference x height = 2(pi)r x 2r = 4(pi)r^2 Therefore, the surface area of a sphere is equivalent to the formula above, or 4(pi)r^2. Are you mind-blowned like me? I know, mathematics has its own way of surprising us with its theories. Good luck,
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