A cone has a slant length of 5 and a diameter of 4. What is the volume of the cone? Use π ≈ 3.14.
2 answers:
Answer:
V = 19.19 cubic units
None of the options are correct.
Step-by-step explanation:
Volume of a cone is given as;
V = ⅓πr²h
Now, we are given;
diameter = 4 units
Thus radius;r = diameter/2 = 4/2 = 2 units
I have attached an image to show the diagram of the cone.
Now, to find the height (h), we know the radius(r) and we know the slant length(l) . So we can use Pythagoras theorem to find the height.
From Pythagoras theorem;
r² + h² = l²
Where l is the hypotenuse or the slant side while "r" is the radius of the cone while the height will be "h"
Thus;
2² + h² = 5²
h² = 5² - 2²
h² = 25 - 4
h² = 21
h = √21
h = 4.5826 units
So height (h) = 4.5826 units
Volume of cone;V = ⅓πr²h
We are told that π = 3.14
Thus;
V = ⅓ x 3.14 x 2² x 4.5826
V = 19.19 cubic units
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Answer:
0.0322; 0.9929
Step-by-step explanation:
Since the data is normally distributed, we use z scores for these probabilities.
The formula for a z score of a sample mean is
For the sample of mildly obese people, the mean, μ, is 371; the standard deviation, σ, is 65; and the sample size, n, is 6.
Using 420 for X,
z = (420-371)/(65÷√6) = 49/(65÷2.4495) = 49/26.5360 ≈ 1.85
Using a z table, we see that the area under the curve to the left of this is 0.9678. However, we want the area to the right, so we subtract from 1:
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Using 420 for X, we have
z = (420-528)/(108÷√6) = -108/(108÷2.4495) = -108/44.0906 ≈ -2.45
Using a z table, we see that the area under the curve to the left of this is 0.0071. We want the area under the curve to the right, so we subtract from 1:
1-0.0071 = 0.9929
Answer:
Step-by-step explanation:
Factor the equation using formula for difference of the cubes:
then
1. The equation has real solution
2. The equation has negative discriminant
then it has two complex solutions