1. Name the two-dimensional shapes that when rotated around the vertical axis form the following three-dimensional solids?
Cone:
Cylinder:
Sphere:

2. Name four, three-dimensional solid objects found in your home, workplace, etc. , and tell what geometric solid each most closely represents.

Object 1:

Object 2:

Object 3:

Object 4:

3. State the volume formulas for a cylinder, sphere, pyramid, and cone.
a. Volume formula for a cylinder:

b. Volume formula for a sphere:

c. Volume formula for a pyramid:

d. Volume formula for a cone:

Problem 1

Answers:

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Explanation:

Imagine a fan blade rotating. As it rotates really quickly, it occupies a 3D space. Or perhaps imagining rotating eggbeaters is a better thing to have in mind. Those blades spin really fast to form a 3D shape. So that's what's going on with this problem. If you spin a triangle around an axis, a cone will form. The base of the triangle forms the base of the cone. Half the base of the triangle is the radius of the cone. The height of the triangle is the height of the cone.

Similarly, a rectangle rotated around its center axis forms a cylinder. Think of a revolving door. That's often a classic example. Finally, a circle spun around any of its diameters will form a sphere.

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Problem 2

Answers:

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Explanation:

Pick objects around your house that are fairly simple in design and resemble either a cylinder, sphere, or cone. A cup resembles a cylinder just it doesn't have a top to it. A ball is a 3D sphere that has an interior to it, unless the ball is filled with air. A funnel resembles a cone due to its triangular shape of sorts. A paper towel roll (the card board piece or the cardboard plus the actual paper towels) resemble a cylinder as well. You can pick any four other objects you have around your house such as a cylindrical speaker, batteries (shaped as a cylinder), soup cans (also cylinders), and so on.

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Problem 3

Answers:

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Explanation:

These formulas are what you should memorize or have handy on a flashcard. It is possible to derive them, but it would require calculus to do so. Also, such a process is quite length. So memorization or flashcards are the better way to go.

For the cylinder and cone, r is the radius and h is the height. Note how the formulas are nearly identical except the cone has the (1/3) term. This shows that the cone's volume is 1/3 that of the cylinder's volume where they both have the same radius r and height h.

The sphere also deals with the radius r, but we don't have to worry about the height of the sphere (it's really just 2r).

For the pyramid, L,W,H represent the length width and height respectively. The length and width form the base of the pyramid. Recall that L*W*H is the volume of a rectangular block. The volume of a pyramid is 1/3 of that rectangular block's volume.

If all of a 2D object's sides and angles have different lengths, such shape is said to be irregular.

In geometry, a form or figure having length and breadth is referred to as a "2D shape." Due to the lack of a thickness, a third dimension, such as the case of a prism or a cube, two-dimensional or 2D objects are often measured in terms of their two faces.

'2D' refers for 2-dimensional. A 2D shape is any form that has two dimensions. Consider for a moment what it means to have two dimensions. We could only move backwards or forwards in a straight line if we only had one dimension to work with. One dimension is a line.

Cone: Triangle

Cylinder: Rectangle

Sphere: Circle

Therefore, if all of a 2D object's sides and angles have different lengths, such shape is said to be irregular.

To know more about 2D shape, here:

https://brainly.com/question/30162250

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