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mina [271]
4 years ago
6

An automobile engineer is redesigning a conical chamber that was originally specified to be 12 inches long with a circular base

of diameter 5.7 inches. In the new design, the chamber is scaled by a factor of 1.5. The volume of the original chamber is a.)102.02 b.)248.04 c.)306.06 d.)412.08 cubic inches. This is a.)242.47 b.)344.49 c.)432.16 d.)448.21 cubic inches less than the volume of the new chamber.
Mathematics
2 answers:
Veseljchak [2.6K]4 years ago
6 0
The answers are: 
a.)102.02
a.)242.47 

The volume of the cone can be expressed as:
V =   \frac{1}{3} \pi  r^{2} h
where:
V - the volume of the cone,
r - the radius of the cone,
h - the height of the cone.

It is given:
h = 12 in
R = 2r = 5.7 in     ⇒     r = 5.7 in ÷ 2 = 2.85 in
π = 3.14

Therefore, the volume of the original conical chamber (V₁)
V =  \frac{1}{3} *3.14*(2.85) ^{2} *12 = 3.14*8.1225*4 = 102.02 in^{3}


Further, the new chamber is scaled by a factor of 1.5. That means that radius and height of the original chamber are increased 1.5 times:
r₁ = r · 1.5 = 2.85 in · <span>1.5 = 4.275 in
</span>h₁ = h · 1.5 = 12 in · <span>1.5 = 18 in
</span>
The volume of the new chamber is:
V_1= \frac{1}{3} *3.14*(4.275) ^{2} *18 = 3.14*18.28*6=344.49 in ^{3}

The difference between two chambers is:
V₁ - V = 344.49 - 102.02 = 242.47

anastassius [24]4 years ago
5 0

Answer:

a and a

Step-by-step explanation:

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PLEASE HELP!!!:
stiks02 [169]

The volume of premium antifreeze to be used is 60 gallons.

The volume of water to be used is 120 gallons

<h3>What is a percentage?</h3>

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Let the volume of 60% pure antifreeze be used to make 20% pure antifreeze.

= x gallons  

The volume of 20% pure antifreeze = 180 gallons

For 60% pure antifreeze:

C₁ = 60% , V₁ = x gallons

For 20% pure antifreeze :

C₂ = 20% , V₂ = 180  gallons

Applying,

C₁V₁ = C₂V₂

60 × x = 20 × 180

x = 60 gallons

The volume of 60% pure antifreeze used = 60 gallons.

The volume of water to be used.

= 180 - 60 gallons

= 120 gallons

Thus,

The volume of premium antifreeze to be used is 60 gallons.

The volume of water to be used is 120 gallons

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5 0
1 year ago
Solve these multi step equations. Show your work. Justify each of your steps. 3x+4+6x=12-41+6x
Lena [83]

Answer:

x=11

Step-by-step explanation:

Combine like terms:

3x +4 +6x =12- 41+ 6x

9x +4 =12 -41 + 6x

Subtract the numbers:

9x+ 4= 12- 41+ 6x

9x + 4= -29 +6x

Rearrange terms:

9x+4=-29+6x

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3 years ago
A school is going to a field trip to the zoo. There were S amount of students. The tickets are 15 dollars each. The school ended
NikAS [45]
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3 0
3 years ago
Cuál es la solución de la ecuación 9 x + 1 = 2x + 15
arsen [322]

Answer:

X=2

Step-by-step explanation:

9x+1=2x+15

1. restar 1 de ambos lados  ejemplo: 9x+1-1=2x+15-1

2. simplificar Ejemplo: 9x=2x+14

3. restar 2x de ambos lados ejemplo: 9x-2x=2x-2x+14

4. simplificar ejemplo: 7x=14

5.divide ambos lados entre 7 ejemplo: 7x/7= 14/7

6.Simplificar ejemplo: x=2

3 0
3 years ago
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