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3 years ago

Find the diameter of a cone that had a volume of 56.52 cubic inches and a height of 6 inches

Mathematics

2 answers:

bulgar [2K]3 years ago

5 0

Answer: 5.98 inches

Step-by-step explanation:

1. You have that the formula for calculate the volume of a cone is:

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

Where V is the volume, r is the radius and h is the height.

2. By definition, the diameter is twice the radius. Therefore, you need to solve for the radius:

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

3. Substitute values:

$r=\sqrt{\frac{3(56.52in^{3})}{(6in)\pi}}=2.99in$

4. The diameter is:

$D=2r\\D=2(2.99in)\\D=5.98in$

aev [14]3 years ago

4 0

Answer:

6 inches

Step-by-step explanation:

The volume of a cone is 1/3 $\pi r^2h$ . We are given the volume and height, so substitute these values in and then solve for r. The radius is half of the diameter, so multiply the radius by two in the end to find the diameter.

1/3 $\frac{1}{3} \pi r^2(6)=56.52$

Multiply 1/3, pi, and 6 together.

$6.29r^2=56.52$

Divide both sides by 6.29.

$r^2=8.99$

Square root both sides.

r = 2.998

Multiply the radius 2.998 by 2 to find the diameter.

2.998 * 2 = 5.996

Since the volume was given in the hundredths place, we will round 5.996 to the hundredths: 6.

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The difference of the fraction is $\mathbf{ -\dfrac{3}{4}}$ by using equivalent expressions.

<h3>What is a number line?</h3>

A number line is a diagrammatic representation of real numbers on the graduated line. It ranges from negative axis to positive axis with 0 being the center position.

A sketch showing the representation of the difference in the mixed fractions can be seen in the image attached below.

Using equivalent expressions to determine the difference between the mixed fractions, we have;

$\mathbf{ = -2\frac{1}{2} - (-1\dfrac{3}{4}) }$

$\mathbf{ = -2\frac{1}{2} +1\dfrac{3}{4} }$

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2 years ago

Write the point-slope form of the equation of the line through the given point with the given

UNO [17]

Answer:

The point-slope form of the equation is:

$y-\left(-5\right)=-3\left(x-3\right)$

Step-by-step explanation:

Given

point (3, -5)

slope = -3

We know the point-slope form of the line equation is

$y-y_1=m\left(x-x_1\right)$

where m is the slope

substituting the values m = -3 and the point (3, -5)

$y-y_1=m\left(x-x_1\right)$

$y-\left(-5\right)=-3\left(x-3\right)$

Thus, the point-slope form of the equation is:

$y-\left(-5\right)=-3\left(x-3\right)$

6 0

3 years ago

Please Help! i need explanations too. Thank you

Lady bird [3.3K]

Answer:

Step-by-step explanation:

The most important thing to remember when solving equations is whatever you do to one side, you must do to the other.

1. (15m + 3)/2 = -6

First, we can simplify by removing the fraction:

15m + 3 = -6 x 2 (multiply both sides by 2)

15m + 3 = -12

15m = -12 - 3 (subtract by 3 on both sides)

15m = -15

m = -15/15 (divide by 15 on both sides)

m = -1

2. 3/2x -15 = -12

first, we'll add both sides by 15

2/3x = -12 + 15

2/3x = 3

x = 3/(2/3) both sides divided by 2/3, just put that in your calculator, if you can't do it in your head

x = 4 1/2

3. -7x + 3 = -15/2

We can remove the fraction by doing the same thing as in the first question.

2(-7x + 3) = -15

-14x + 6 = -15

14x = -15 -6

14x = -21

x = -21/14

x = -1 1/2

4. 4x + 1/2(12x + 2) = 3

First we need to simplify by expanding:

4x + 6x + 1 = 3

Now we collect the like terms to further simplify the equation

10x + 1 = 3

10x = 3 - 1

10x = 2

x = 2/10

x = 1/5

5. 3/2(x + 8) = 6x

We're going to start by removing the brackets, this time by multiplying the fraction on both sides:

x + 8 = 6x / (3/2)

x + 8 = 4

x = 4 - 8

x = -4

Now the questions, some of them are personal, so I won't be able to answer them for you, but I can try with the others:

These types of problems are fractional equations, and you need to find the value of the variable, which in this case was x.

I'm not sure what information you already know, so you'll have to think on that one.

Strategies you could use or try include multiplying, dividing, subtracting and adding on both sides as well as collecting like terms and expanding.

Hope this helped,

Cate

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3 years ago

Find each percent of change. Round to the nearest whole percent if necessary. State whether the percent of change is an increase

Alex787 [66]

So first we see if increase or decrease
180<210
it is increase

then we assume that
percent change
find how much change took place
210-180=30
30/180=x% change
percent means parts out ofo 100s so x%=x/100
30/180=x/100
multiply both sides by 100
3000/180=x
16.66666=x
answe ris 16.6%

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