Answer:
1331:216
Step-by-step explanation:
Given the ratio of the lengths of two similar solids as a:b
The ratio of the surface areas =
The ratio of the volume =
We are given that the ratio of the surface areas of two similar geometrical solids is given by 121:36
Therefore:
Since the ratio of the lengths is 11:6
The ratio of their volumes =
=1331:216
The ratio of the volume of the two similar geometrical solids is 1331:126.
Answer:
Step-by-step explanation:
The identities you need here are:
and
You also need to know that
x = rcosθ and
y = rsinθ
to get this done.
We have
r = 6 sin θ
Let's first multiply both sides by r (you'll always begin these this way; you'll see why in a second):
r² = 6r sin θ
Now let's replace r² with what it's equal to:
x² + y² = 6r sin θ
Now let's replace r sin θ with what it's equal to:
x² + y² = 6y
That looks like the beginnings of a circle. Let's get everything on one side because I have a feeling we will be completing the square on this:
Complete the square on the y-terms by taking half its linear term, squaring it and adding it to both sides.
The y linear term is 6. Half of 6 is 3, and 3 squared is 9, so we add 9 in on both sides:
In the process of completing the square, we created within that set of parenthesis a perfect square binomial:
And there's your circle! Third choice down is the one you want.
Fun, huh?