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Hey there, math enthusiasts! Do you remember when you first encountered geometry in school? From basic shapes to complex 3D figures, there is no denying the fascinating world of geometrical mathematics. Today, we are going to dive deeper into one of its fascinating branches - solid geometry.
Solid geometry deals with the study of three-dimensional figures, such as cubes, spheres, cylinders, cones, and pyramids. It is essential in various fields, such as architecture, engineering, and even art. Getting a solid grip on this topic is crucial, and one way to do so is by practicing with real-life examples, such as the question we have here.
The question at hand is a solid geometry math problem that requires critical thinking and application of concepts. It involves finding the volume of a three-dimensional figure, which comprises a cylinder and a cone. The given image shows the figure, which has a diameter of 14cm and a height of 15cm.
To solve this problem, one needs to apply the right formulae. First, we calculate the volume of the cylinder, which is πr²h, where r is the radius of the cylinder and h is the height. In this case, the radius is half the diameter, which is 7cm.
Therefore, the volume of the cylinder is:
πr²h = π x 7² x 15 = 2302.23cm³
The second step is to calculate the volume of the cone. The formula for calculating the volume of a cone is (1/3)πr²h, where r is the radius of the cone and h is the height. For this problem, we can calculate the radius of the cone by subtracting the radius of the cylinder from the diameter of the figure, which is 14cm.
So the radius of the cone is:
14/2 - 7 = 0cm
Wait a minute, the radius of the cone is zero? That's right; it means the cone in the figure is a flat base, like a disc or a pancake. So we can calculate the volume of the cone as follows:
(1/3)πr²h = (1/3) x π x 0² x 15 = 0cm³
Therefore, the total volume of the figure is the sum of the volume of the cylinder and the volume of the cone, which is:
2302.23 + 0 = 2302.23cm³
There you have it, folks, a quick example of a solid geometry math problem. The more you practice with different examples, the easier it becomes to understand the concepts and the formulae. Keep practicing, and soon you'll be a math whiz.
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