Answer:
Volume of the frustum = 225.0952
Surface area = 274
Step-by-step explanation:
The volume can be calculated as the difference of the complete pyramid and the tip of the pyramid.
To find the height of the frustum, we can use pythagoras theorem in the following triangle:
first side: 9 - 5 = 4
second side h (height)
hypotenusa: slang = 6
6^2 = h^2 + 4^2
h^2 = 36 - 16 = 20
h = 4.4721
To find the height of the complete pyramid (H), we can use the following rule of three:
H / 9 = (H - 4.4721) / 5
5H = 9H - 40.2489
4H = 40.2489
H = 10.0622
Volume of complete pyramid:
V_complete = (1/3)*9^2*10.0622 = 271.6794
Volume of the tip:
V_tip = (1/3)*5^2*(10.0622 - 4.4721) = 46.5842
Volume of the frustum:
V_frustum = V_complete - V_tip = 225.0952
The surface area is the bigger base area + smaller base area + four side areas.
Bigger base area = 9^2 = 81
Smaller base area = 5^2 = 25
Side area = (9+5)*6/2 = 42
Total surface area: 81 + 25 + 4*42 = 274
Answer:
Step-by-step explanation:
The vertical angles have the same measure, so ...
3x +50 = 6x -10
60 = 3x . . . . . add 10-3x
20 = x . . . . . . divide by 3
Answer:
No
Step-by-step explanation:
Let's check the first statement with an example. 2 and 3 are positive numbers and their sum (5) is also positive so his first statement is true.
To check the second statement let's look at the negative numbers -1 and -8 for example. Their sum (-9) is also negative so his second statement is true.
To check the third statement let's look at the numbers 9 and -5. One is positive and one is negative, but their sum (4) is positive, so his third statement is false. However if we look at the numbers 4 and -7, their sum is negative so the third statement is partially false.
Answer
The scale factor is
Explanation
We have to ways to find the scale factor here:
1. Find the unit fraction from inches to miles; in other words, we need to divide the distance between the cities on the map (in inches) by the actual distance between the cities.
We can conclude that the scale factor is
2. Let be the scale factor.
We know form our problem that 24 miles times the scale factor is equal 4 1/2 inches, so we can set up an equation an solve for :
Just like before, we can conclude that the scale factor is
B.
Answer
6 inches separate the cities on the map
Explanation
We know that our scale factor is 1/4 inch = 1 mile, so we can create a conversion factor to convert 24 miles to inches. Since we need to convert from miles to inches, the denominator of our conversion factor must be 1 mile so we can cancel miles out. Notice that we can also express 1/4 inch as 0.25 inch to simplify our calculations:
We can conclude that if the conversion factor is 1/4 inch = 1 mile, 6 inches separate the cities on the map.
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Answer:
Answer is B. angle addition postulate
Step-by-step explanation:
-UvU-
