Geometry - Volume and Surface Area

12 important questions on Geometry - Volume and Surface Area

True or false: where in 2D we talked about the are of shapes, we will also talk talk about volume when it comes to 3d shapes.

True

What is formula for the volume of a cube?

If S represents something called the edge length (more on that later), the its S^3.

What are rectangular solids?

Rectangular solids is a general category under which 3d shapes like the cube fall.
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Within the 'rectangular solids' catgeory, how do you calculate the volume?

Volume is the product of the 3 different edge lengths:
Volume = height * weight * depth

Within the 'rectangular solids' catgeory, how do you calculate the total surface area?

Total surface area = 2 hw + 2hd + 2wd.
With h = height, w = width, and d = depth.

Within the 'rectangular solids' catgeory, why does the formula for the total surface area contain coefficients of 2 (2hw + 2hd + 2wd).

Because the entire area consists of 2 of each (hw, hd and wd) surfaces.

In a rectangular solid, how many different kinds of diagonals can we consider?

Two:
1) A face diagonal
2) A space diagonal

How do you find the length of a face diagonal?

Because it pertains to only one face and is in that sense exactly like with a 2D surface area, we can use what we already know: the pythagorean theorem.

What is a space diagonal?

As opposed to with a face diagonal, a space diagonal does not run along a face: it is diagonal from whatever way you look at it: from above and the side as well.

How do you find the length of a space diagonal?

Get this: you use the 3D version of the pythagorean theorem.

What is the formula for the volume of a cylinder?

The volume for a cylinder is basically area of the base x the height.
The base in itself is pi*r^2.
So Volume of a cylinder = base * height = (pi*r^2) * height

What is the formula for the volume of a sphere (not required info for the test so you can skip this question if you want)?

Volume = (4/3)*pi*r^3

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