Question 1163037: 1. The surface areas of two similar cylinders are 6pift^2 and 54pift^2. The volume of the smaller cylinder is 2pift^3. What is the volume in cubic feet of the larger cylinder?
a. 108pi
b. 54pi
c. 27pi
d. 18pi, my answer
2.Which of the following shows a top, front, and right-side view of a 3-D shape?
a. an isometric drawing
b. an orthographic drawing, my answer
c. a foundation drawing
d. a net
3. Which type of drawing can be used to show three sides of a solid from a corner view?
a. an isometric drawing, my answer
b. an orthographic drawing
c. a foundation drawing
d. a net
4. Line AB has endpoints A (x, y, z) and B (−2, 6, 13) and midpoint M (2, −6, 3). What are the coordinates of A?
a. A (−6, 18, 23)
b. A (0, 0, 8)
c. A (2, −6, 19)
d. A (6, −18, −7), my answer
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
Problem 1
The two surface areas are in ratio
6pi : 54pi
This reduces to the ratio
1 : 9
after dividing both parts by 6pi.
The ratio 1:9 means that the larger area is 9 times that of the smaller area.
So the linear scale factor is sqrt(9) = 3. Meaning the larger object has a radius 3 times that of its smaller counterpart, and same with the height as well.
We can represent this as the ratio 1:3
The ratio 1 : 3 cubes to 1 : 27 telling us that the larger object's volume is 27 times larger than the smaller object's volume.
The smaller cylinder has volume 2pi. Multiply this with 27 to get the volume of the larger cylinder.
Answer: B. 54pi cubic feet
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Problem 2
You are correct.
An orthographic drawing is one where we see three views of the top, front and right sides of the 3D object. Each portion is flat or 2D. When combined, they will help us form a 3D object in our head, which the isometric drawing represents. An isometric drawing is done alongside the orthographic portion, so two complement one another.
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Problem 3
You are correct here as well.
This is a single view angled down where we can see three sides at a time (top, front, right). It's basically an orthographic drawing but all three portions are combined into one.
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Problem 4
You are correct.
The idea is to add the endpoint coordinates and divide by 2
x coordinate of midpoint = (x1+x2)/2
y coordinate of midpoint = (y1+y2)/2
z coordinate of midpoint = (z1+z2)/2
Where we know the midpoint coordinates and only one of the endpoint coordinates. So we'll have to use a bit of algebra to get the answer.
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