Answer:
See example below.
Step-by-step explanation:
The image of a triangle will be 5/6 the size. It will be slightly smaller than the original. For example, if the side measurement of the triangle on one side is 12 then the image of the triangle after a dilation will be 12*5/6 = 60/6 = 10.
The new side length is 10 slightly smaller than 12.
Answer:
180 cubes
Step-by-step explanation:
little cubes:

The prism:

the number of cubes that fill the prism:

Hope this helps
They probably thought square rotting was dividing by 2. The correct answer is about 20
Volume of a cylinder is

, where r is the radius and h is the height.
This comes from the area of a circle being

. A cylinder is the area of the base circle multiplied by its height.
Using this formula, the volume of the given cylinder is
Another triple integral. We're integrating over the interior of the sphere

Let's do the outer integral over z. z stays within the sphere so it goes from -2 to 2.
For the middle integral we have

x is the inner integral so at this point we conservatively say its zero. That means y goes from
and 
Similarly the inner integral x goes between 
So we rewrite the integral

Let's work on the inner one,

There's no z in the integrand, so we treat it as a constant.

So the middle integral is
I gotta go so I'll stop here, sorry.