What is 45*90<br><br><br><br>Answer: 4,050

The volume of a right circular cone with radius r and height h is V = pir^2h/3.

Scorpion4ik [409]

The question is incomplete. The complete question is :

The volume of a right circular cone with radius r and height h is V = pir^2h/3. a. Approximate the change in the volume of the cone when the radius changes from r = 5.9 to r = 6.8 and the height changes from h = 4.00 to h = 3.96.

b. Approximate the change in the volume of the cone when the radius changes from r = 6.47 to r = 6.45 and the height changes from h = 10.0 to h = 9.92.

a. The approximate change in volume is dV = _______. (Type an integer or decimal rounded to two decimal places as needed.)

b. The approximate change in volume is dV = ___________ (Type an integer or decimal rounded to two decimal places as needed.)

Solution :

Given :

The volume of the right circular cone with a radius r and height h is

$V=\frac{1}{3} \pi r^2 h$

$dV = d\left(\frac{1}{3} \pi r^2 h\right)$

$dV = \frac{1}{3} \pi h \times d(r^2)+\frac{1}{3} \pi r^2 dh$

$dV = \frac{2}{3} \pi r h (dr)+\frac{1}{3} \pi r^2 dh$

a). The radius is changed from r = 5.9 to r = 6.8 and the height is changed from h = 4 to h = 3.96

So, r = 5.9 and dr = 6.8 - 5.9 = 0.9

h = 4 and dh = 3.96 - 4 = -0.04

Now, $dV = \frac{2}{3} \pi r h (dr)+\frac{1}{3} \pi r^2 dh$

$dV = \frac{2}{3} \pi (5.9)(4)(0.9)+\frac{1}{3} \pi (5.9)^2 (-0.04)$

$dV=44.484951 - 1.458117$

$dV=43.03$

Therefore, the approximate change in volume is dV = 43.03 cubic units.

b). The radius is changed from r = 6.47 to r = 6.45 and the height is changed from h = 10 to h = 9.92

So, r = 6.47 and dr = 6.45 - 6.47 = -0.02

h = 10 and dh = 9.92 - 10 = -0.08

Now, $dV = \frac{2}{3} \pi r h (dr)+\frac{1}{3} \pi r^2 dh$

$dV = \frac{2}{3} \pi (6.47)(10)(-0.02)+\frac{1}{3} \pi (6.47)^2 (-0.08)$

$dV=-2.710147-3.506930$

$dV= -6.22$

Hence, the approximate change in volume is dV = -6.22 cubic units

8 0

2 years ago

The tests done to determine if someone is HIV positive are called Enzyme immunoassay or

Blizzard [7]

The answer would be answer choice B.

8 0

3 years ago

A cylinder and a cone are shown below.

Veronika [31]

Answer:

36 in³

Step-by-step explanation:

Volume of cylinder = pi×r²×h

Volume of cone = ⅓×pi×r²×h

For same r and h,

Volume of cone is ⅓ of the Volume of cylinder

⅓ × 108 = 36

3 0

2 years ago

Help solving this math question

olga_2 [115]

22. B) $65,000,000 per year.

23. B) Education.

Step-by-step explanation:

Step 1; To find the average rate of change in annual budget between the two given years. We divide the difference in values for the two years by the period in between the two years. In 2008, the budget was $358,708,000 while in 2010 it was $488,106,000. The period in between was 2 years i.e 2009 and 2010.

The average rate of change = $\frac{488,106,000-358,708,000}{2}$ = $\frac{129,398,000}{2}$ = $64,699,000 per year.

So the average rate of change was $64,699,000 which approximately equals option B. $65,000,000.

Step 2; To find the human resources program's 2007 to 2010 ratio we divide the value in 2007 to the value in 2010. To find the other similar ratio, we divide the value in 2007 to the value in 2010 for all the other programs and determine which is closest to the human resources program.

Human resources program ratio = $\frac{4,051,050}{5,921,379}$ = 0.6841,

Agricultural / natural resources ratio = $\frac{373,904}{488,106}$ = 0.766,

Education's ratio = $\frac{2,164,607}{3,008,036}$ = 0.7196,

General government's ratio = $\frac{14,347,325}{14,716,155}$ = 0.9749,

Highways and transportation's ratio = $\frac{1,468,482}{1,773,893}$ = 0.827,

Public safety's ratio = $\frac{263,463}{464,233}$ = 0.5675.

The Human resources' program ratio is 0.6841 and the closest is Education's ratio which is 0.7196. So education is the answer.

4 0

2 years ago

Convert 2/3 to a decimal by long division

PilotLPTM [1.2K]

2÷3 3 goes into 2 0 times so add 0 to make 20 3goes into 20 6 time so the answer is 0.6666666

7 0

3 years ago

What is 45*90Answer: 4,050