Comparing Volume- Which of These Solids – 8, 3, 6, or 2 – Has the Greatest Capacity-
Which solid has a greater volume: 8, 3, 6, or 2? This question may seem straightforward, but it requires a deeper understanding of geometric shapes and their respective volumes. In this article, we will explore the volumes of different solids and determine which one among the given numbers has the greatest volume.
Solid geometry is a branch of mathematics that deals with the properties of three-dimensional figures. The volume of a solid is a measure of the space it occupies. To find the volume of a solid, we need to know its dimensions, such as length, width, and height. In this case, we are given four numbers: 8, 3, 6, and 2. These numbers could represent the dimensions of different solids, and our task is to identify which solid has the greatest volume.
Let’s consider the possible solids and their dimensions:
1. Cube: A cube is a three-dimensional figure with all sides of equal length. If the given number 8 represents the length of a side of a cube, then the volume of the cube would be 8^3 = 512 cubic units.
2. Cuboid: A cuboid is a three-dimensional figure with all sides of different lengths. If the given numbers 8, 3, and 6 represent the length, width, and height of a cuboid, respectively, then the volume of the cuboid would be 8 3 6 = 144 cubic units.
3. Cylinder: A cylinder is a three-dimensional figure with two parallel circular bases and a curved surface connecting them. If the given numbers 8, 3, and 6 represent the radius of the base, height, and circumference of the base, respectively, then the volume of the cylinder would be π (3^2) 6 = 54π cubic units, which is approximately 169.646 cubic units.
4. Sphere: A sphere is a three-dimensional figure with all points equidistant from its center. If the given number 8 represents the radius of the sphere, then the volume of the sphere would be (4/3) π (8^3) = 2144π/3 cubic units, which is approximately 706.857 cubic units.
Now, let’s compare the volumes of these solids:
– Cube: 512 cubic units
– Cuboid: 144 cubic units
– Cylinder: 169.646 cubic units
– Sphere: 706.857 cubic units
Based on our calculations, the sphere has the greatest volume among the given numbers. Therefore, the answer to the question “Which solid has a greater volume: 8, 3, 6, or 2?” is the sphere, with a volume of approximately 706.857 cubic units.
