Answer:
Step-by-step explanation:
From the way the answers are presented, it can be seen that x refers to the radius of the base of the cone
radius:
and we are told that the height is twice the radius, so:
height:
and now we use the formula to calculate the volume of a cone:
where is volume,
is radius, and
is the height. and
is a constant
in this case
so we substitute thisvalues in the formula for the volume:
Rearranging the terms
which is option A.
Your Question was incomplete so I will solve a similar question that will help you to tackle this kind of questions.
Q)Two university female basketball players are being considered for an award to be given to the most consistent player with the highest scoring average for the season. The number of points scored per game for all games played during the season is given by the following table. ( Table Attached)
a) Calculate the population mean and population standard deviation of the number of points scored per game for each player.
(b) Using the results of part (a) which player should receive the award.
Answer:
<h3><u>Player B should receive the award.</u></h3><h3>Step-by-step explanation:</h3>Points of player A:- 5,32,45,25,8,10,35,12,37,21
<u>First we will calculate the mean for player A</u>
∑x = 5 + 32 + 45 + 25 + 8 + 10 + 35 + 12 + 37 + 21
∑x = 230
N = 10
<u>Mean = µ= ∑x/N = 230/10 = 23</u>
<u>Now we will calculate the standard deviation for Player A</u>
x - µ = -18 , 9, 22, 2, -15, -13, 12, 11, 14, -2
(x - µ)^2 = 324, 81, 484, 4, 225, 169, 144, 121, 196, 4
∑(x - µ)^2 = 1752
σ = sqrt( ∑((x - µ)^2/N) )
σ = sqrt(1752/10)
<u>σ = 13.236</u>
<u>Calculating mean for player B:</u>
Points of player B = 18, 20, 22, 15, 35, 24, 29, 19, 25, 23
∑x = 18 + 20 + 22 + 15 + 35 + 24 + 29 + 19 + 25 + 23
N =10
µ = 230/10
<u>µ = 23</u>
<u>Calculating standard deviation for player B:</u>
(x - µ ) = -5, -3, -1, -8, 12, 1, 6, -4, 2, 0
(x -µ )^2 = 25, 9, 1, 64, 144, 1, 36, 16, 4, 0
∑(x - µ)^2 = 300
σ = sqrt(300/10)
<u>σ = 5.48</u>
Since both Player A and Player B have same mean we will calculated the coefficient of variation for both the players.
<u>For player A:</u>
σa/µa *100 = 13.24/23 *100 = 57.56
<u>For Player B:</u>
σb/µb *100 = 5.48/23 * 100 = 23.82
<u>Since the coefficient of variation of Player B is less than Player A hence Player B should receive the award.</u>
