What is the volume of the sphere?
1 answer:
The volume of the sphere in the given image, to the nearest tenth, is: 2,143.6 cm³.
<h3>How to calculate the Volume of a Sphere?</h3>A sphere is a solid shape that is round. The volume of a sphere is the amount of space it contains, which is calculated by the formula expressed as:
Volume = 4/3 × π × r³, where r is the radius of the sphere.
The parameter of the sphere is given below:
Radius of the sphere (r) = 8 cm.
π = 3.14
Substitute r = 8 into 4/3 × π × r³ to find the volume of the sphere
Volume of the sphere = 4/3 × π × r³ = 4/3 × 3.14 × 8³
Volume of the sphere = 4/3 × 3.14 × 512
Volume of the sphere = (4 × 3.14 × 512)/3
Volume of the sphere = (6,430.72)/3
Volume of the sphere = 2,143.6 cm³
In summary, the volume of the sphere in the given image, to the nearest tenth, is: 2,143.6 cm³.
Learn more about the volume of sphere on:
#SPJ1
You might be interested in
The range of the provided inverse sine function in terms of <em>x</em>, and <em>y </em>y = sin-1x is [-π/2, π/2].
<h3>What is the range of the function?</h3>Range of a function is the set of all the possible output values which are valid for that function.
The trigonometry function given in the problem is,
The above function can be written as,
The above function is the arc of sine function. The domain of arc of sine ranges from -1 to 1.
This is the domain of the inverse of sine function. In the attached image below, the graph of inverse sine function is plotted. The range of this function is,
Thus, the range of the provided inverse sine function in terms of <em>x</em>, and <em>y </em>y = sin-1x is [-π/2, π/2].
Learn more about the range of the function here;
Answer:
a) 51.60% probability that in a given year there will be less than 21 earthquakes.
b) 49.35% probability that in a given year there will be between 18 and 23 earthquakes.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
a) Find the probability that in a given year there will be less than 21 earthquakes.
This is the pvalue of Z when X = 21. So
has a pvalue of 0.5160.
So there is a 51.60% probability that in a given year there will be less than 21 earthquakes.
b) Find the probability that in a given year there will be between 18 and 23 earthquakes.
This is the pvalue of Z when X = 23 subtracted by the pvalue of Z when X = 18. So:
X = 23
has a pvalue of 0.7611
X = 18
has a pvalue of 0.2676
So there is a 0.7611 - 0.2676 = 0.4935 = 49.35% probability that in a given year there will be between 18 and 23 earthquakes.