Let r be a radius of a given circle and α be an angle, that corresponds to a sector.
The circle area is
and denote the sector area as
.
Then
(the ratio between area is the same as the ratio between coresponding angles).
.
Answer:
When increasing the radius 3 times the volume increases 9 times and when it is reduced to a third the volume decreases 9 times
Step-by-step explanation:
We have that the formula for the volume of a cone is:
Vc = pi * (r ^ 2) * h
We first calculate the original volume, where the radius is 2 and the height is 9, replacing:
Vc = 3.14 * (2 ^ 2) * 9
Vc = 113.04
Now if the radius is tripled it would be: 2 * 3 = 6, the radius would be 6, replacing:
Vc = 3.14 * (6 ^ 2) * 9
Vc = 1017.36
If we compare:
1017.36 / 113.04 = 9
This means that when the radius is tripled, the volume increases 9 times.
When if re reduces to a third the radius would be: 2/3, replacing:
Vc = 3.14 * ((2/3) ^ 2) * 9
Vc = 12.56
113.04 / 12.56 = 9
Which means that by reducing it to a third the volume becomes 9 times smaller.
Divide sales tax amount over the item's cost
23.1 / 330 = 0.07
Therefore the sales tax is 7%
Answer:
9.7303888 miles
Step-by-step explanation:
Given the following :
Set target = 12 miles per week.
Miles ran on Monday = 4 3/4 miles
Miles ran on Wednesday = 3 1/3 miles
Miles ran on Friday = 1 11/17 miles
Number of miles covered for the week:
(miles covered on Monday + miles covered on Wednesday + miles covered on Friday)
= (4 3/4 + 3 1/3 + 1 11/17) miles
= (19/4 + 10/3 + 28/17) miles
= (4.75 + 3.33333 + 1.6470588) miles
= 9.7303888 miles
