Answer:
Volume of the frustum = ⅓πh(4R² - r²)
Step-by-step explanation:
We are to determine the volume of the frustum.
Find attached the diagram obtained from the given information.
Let height of small cone = h
height of the large cone = H
The height of a small cone is a quarter of the height of the large cone:
h = ¼×H
H = 4h
Volume of the frustum = volume of the large cone - volume of small cone
volume of the large cone = ⅓πR²H
= ⅓πR²(4h) = 4/3 ×π×R²h
volume of small cone = ⅓πr²h
Volume of the frustum = 4/3 ×π×R²h - ⅓πr²h
Volume of the frustum = ⅓(4π×R²h - πr²h)
Volume of the frustum = ⅓πh(4R² - r²)
Answer:
48π or 150.72
Step-by-step explanation:
The radius of the big circle is 8.
We can use that to find the area of the big circle.
Area is πr^2
π(8)^2
64π
Now, we can find the area of the small circle.
The diameter of that is 8, meaning the radius is 4.
πr^2
π(4)^2
16π
Now we subtract the area of the small circle from the area of the big circle to get the area of the shaded region.
64π-16π=48π
As a decimal: 48*3.14=150.72
Answer:
C. Two smaller atoms come together to form a larger atom that is a different element.
Explanation:
Fusion is a reaction in which two nuclei combine to form a nucleus with the release of energy.
Complete Question
A hypothetical population consists of eight individuals ages 13 14 17 20 21 22 24 30 years.
A: what is the probability that a person in this population is a teenager?
B: what is the probability of selecting a participant who is at least 20 years old?
We have that probability that a person in this population is a teenager and probability of selecting a participant who is at least 20 years old is
From the question we are told
A hypothetical population consists of eight individuals ages 13, 14, 17, 20, 21, 22, 24, & 30 years.
a)
Generally the equation for the probability that a person in this population is a teenager is mathematically given as
P(T)=0.38
b)
Generally the equation for the probability of selecting a participant who is at least 20 years old is mathematically given as
P(T')=0.63
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Answer:
k = 11
Step-by-step explanation:
Given the points are collinear then the slopes between consecutive points are equal.
Using the slope formula
m = 
with (x₁, y₁ ) = (5, 1) and (x₂, y₂ ) = (1, - 1)
m = 
= 
= 
Repeat with another 2 points and equate to
with (x₁, y₁ ) = (1, - 1) and (x₂, y₂ ) = (k, 4)
m = 
, then
= ( cross- multiply )
k - 1 = 10 ( add 1 to both sides )
k = 11
