Given:
Compound shape
To find:
The area of the compound shape.
Solution:
The compound shape is splitted into two parallelograms.
<u>Bottom parallelogram:</u>
Base = 7.5 cm
Height = 5 cm
Area of the parallelogram = base × height
= 7.5 × 5
= 37.5 cm²
The area of the Bottom parallelogram 37.5 cm².
<u>Top parallelogram:</u>
Base = 7.5 cm
Height = 4.5 cm
Area of the parallelogram = base × height
= 7.5 × 4.5
= 33.75 cm²
The area of the top parallelogram 33.75 cm².
Compound shape = 37.5 + 33.75
= 71.25 cm²
The area of the compound shape is 71.25 cm².
We can see that there are 5 CDs, each of radius 9 cm
<u>Area occupied by 1 disc:</u>
Area of a circle = πr²
Area of disc = π(9)²
Area of disc = 3.14 * 81 = 254 cm²
<u>Area occupied by 5 discs:</u>
Area occupied by 5 discs = Area occupied by 1 disc * 5
Area occupied by 5 discs = 254 * 5
Area occupied by 5 discs = 1270 cm²
Step-by-step explanation:
q(a) = ½a + 38
The slope of q is ½. So the perpendicular slope is -1/½ = -2.
Write h(x) in point-slope form:
h − (-7) = -2 (x − 12)
h + 7 = -2 (x − 12)
Simplify to get slope-intercept form.
h + 7 = -2x + 24
h = -2x + 17
Problem One
Call the radius of the second can = r
Call the height of the second can = h
Then the radius of the first can = 1/3 r
The height of the first can = 3*h
A1 / A2 = (2*pi*(1/3r)*(3h)] / [2*pi * r * h]
Here's what will cancel. The twos on the right will cancel. The 3 and 1/3 will multiply to one. The 2 r's will cancel. The h's will cancel. Finally, the pis will cancel
Result A1 / A2 = 1/1
The labels will be shaped differently, but they will occupy the same area.
Problem Two
It seems like the writer of the problem put some lids on the new solid that were not implied by the question.
If I understand the problem correctly, looking at it from the top you are sweeping out a circle for the lid on top and bottom, plus the center core of the cylinder.
One lid would be pi r^2 = pi w^2 and so 2 of them would be 2 pi w^2
The region between the lids would be 2 pi r h for the surface area which is 2pi w h
Put the 2 regions together and you get
Area = 2 pi w^2 + 2 pi w h
Answer: Upper left corner <<<<< Answer
This is what I did for factoring. Let me know if you need more work?
