a round cake is cut into sectors for nine friends, (including jack) at jacks birthday party. after the cake is cut there is no cake remaining, what will be the angle at the centre of the cake for jacks piece if:
a) jack receives twice as much as everyone else? (in parts b and c assume his friends have equal shares of the rest.)
b) jake receives four times as much as everyone else?
c)jake receives ten times as much as everyone else?
(a) 8x+2x = 360
Jack gets 2x
(b) 8x+4x = 360
(c) 8x+10x = 360
there are 8 people who get an equal share, so their angle in the pie chart is x degrees. The sum of all the angles is, of course a whole circle: 360 degrees.
Jack's share (and angle) is 2x,4x, or 10x
so now just find x in each case, and you have your necessary information. Did you actualy read the problem?
hi oobleck
what does 'x' mean?
a) Well, if Jack receives twice as much as everyone else, we can start by imagining each friend's piece as a 1/9th sector of the cake. Since Jack gets twice as much, we need to calculate his portion. If each friend gets 1/9th, then Jack gets 2/9ths.
To find the angle at the center of Jack's piece, we need to find what fraction 2/9ths is of the total angle of the cake. Since the cake is a full circle (360 degrees), we multiply 360 by 2/9:
360 * 2/9 = 80 degrees.
So, the angle at the center of Jack's piece would be 80 degrees.
b) If Jack receives four times as much as everyone else, we apply the same logic as before. Each friend gets 1/9th, so Jack gets 4/9ths.
To find the angle at the center of Jack's piece, we calculate:
360 * 4/9 = 160 degrees.
Therefore, the angle at the center of Jack's piece would be 160 degrees.
c) Finally, if Jack receives ten times as much as everyone else, the calculations stay the same. Each friend gets 1/9th, so Jack gets 10/9ths.
Finding the angle at the center of Jack's piece:
360 * 10/9 = 400 degrees.
Hence, the angle at the center of Jack's piece would be 400 degrees.
To find the angle at the center of the cake for Jack's piece in each scenario, we need to divide the total angle of a full circle (360 degrees) by the number of sectors.
a) If Jack receives twice as much cake as everyone else:
In this case, Jack will have 2 parts of the cake, while his eight friends will each have 1 part. Since the total number of parts is 9, we can calculate Jack's share as follows:
Total number of parts = 9
Jack's parts = 2
Jack's share of the cake = Jack's parts / Total number of parts = 2 / 9
To find the angle at the center of Jack's piece, we multiply Jack's share by the total angle of a full circle:
Angle at center of Jack's piece = Jack's share * 360 degrees = (2 / 9) * 360 degrees
b) If Jack receives four times as much cake as everyone else:
In this case, Jack will have 4 parts of the cake, while his eight friends will each have 1 part. The total number of parts is still 9, so we can calculate Jack's share as follows:
Total number of parts = 9
Jack's parts = 4
Jack's share of the cake = Jack's parts / Total number of parts = 4 / 9
To find the angle at the center of Jack's piece, we multiply Jack's share by the total angle of a full circle:
Angle at center of Jack's piece = Jack's share * 360 degrees = (4 / 9) * 360 degrees
c) If Jack receives ten times as much cake as everyone else:
In this case, Jack will have 10 parts of the cake, while his eight friends will each have 1 part. The total number of parts is still 9, so we can calculate Jack's share as follows:
Total number of parts = 9
Jack's parts = 10
Jack's share of the cake = Jack's parts / Total number of parts = 10 / 9
To find the angle at the center of Jack's piece, we multiply Jack's share by the total angle of a full circle:
Angle at center of Jack's piece = Jack's share * 360 degrees = (10 / 9) * 360 degrees