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leonid [27]
3 years ago
10

A cone and its dimensions are shown in the diagram. What is the volume of the cone in cubic inches?

Mathematics
1 answer:
Vinvika [58]3 years ago
4 0

Answer:

The exact value of the volume is equal to

V=19\frac{397}{512}\pi\ in^{3}

Step-by-step explanation:

we know that

The volume of a cone is equal to

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

we have

D=5\frac{5}{8}\ in

convert to an improper fraction

D=5\frac{5}{8}\ in=\frac{5*8+5}{8}=\frac{45}{8}\ in

r=(45/8)/2=\frac{45}{16}\ in

h=7\frac{1}{2}\ in=\frac{7*2+1}{2}=\frac{15}{2}\ in

substitute in the formula of volume

V=\frac{1}{3}\pi (\frac{45}{16}^{2})(\frac{15}{2})=\frac{30,375}{1,536}\pi\ in^{3}

Simplify  

\frac{30,375}{1,536}=\frac{29,184}{1,536}+\frac{1,191}{1,536}=19\frac{397}{512}

substitute

V=19\frac{397}{512}\pi\ in^{3}

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The area of the square is greater than the circle: the area of the circle is pi(r)^2 while the area of the square is length times width. The area of the circle is about 12.5 while the area of the square is 16.
4 0
3 years ago
When Hailey commutes to work, the amount of time it takes her to arrive is normally distributed with a mean of 21 minutes and a
miskamm [114]

Answer: 135 days

Step-by-step explanation:

Since the amount of time it takes her to arrive is normally distributed, then according to the central limit theorem,

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = standard deviation

From the information given,

µ = 21 minutes

σ = 3.5 minutes

the probability that her commute would be between 19 and 26 minutes is expressed as

P(19 ≤ x ≤ 26)

For (19 ≤ x),

z = (19 - 21)/3.5 = - 0.57

Looking at the normal distribution table, the probability corresponding to the z score is 0.28

For (x ≤ 26),

z = (26 - 21)/3.5 = 1.43

Looking at the normal distribution table, the probability corresponding to the z score is 0.92

Therefore,

P(19 ≤ x ≤ 26) = 0.92 - 28 = 0.64

The number of times that her commute would be between 19 and 26 minutes is

0.64 × 211 = 135 days

8 0
3 years ago
What is an equation of the line that passes through the point (1,-3) and is perpendicular to the line x+3y=21
docker41 [41]

The linear equation that is perpendicular to the line x+3y=21 is:

y = 3*x - 6

<h3>How to find the equation of the line?</h3>

A general line in the slope-intercept form is written as:

y = m*x + b

Where m is the slope and b is the y-intercept.

Two linear equations are perpendicular if the product between the two slopes is equal to -1.

Rewriting the given line we can get:

x +3y = 21

3y = 21 - x

y = 21/3 - x/3

y = (-1/3)*x + 21/3

Then the slope is (-1/3), if our line is perpendicular to this one, then:

m*(-1/3) = -1

m = 3

our line is:

y = 3*x + b

To find the value of b, we use the fact that our line passes through (1, - 3)

-3 = 3*1 + b

-3 - 3 = b

-6 = b

The line is y = 3*x - 6

Learn more about linear equations:

brainly.com/question/1884491

#SPJ1

3 0
1 year ago
Say a population of fish triples every year. The population started with 5 fish. How many years will it
Lostsunrise [7]

Answer:

It should take 10 years

Step-by-step explanation:

In 1 year, if it triples, it should be 15 (population), and so on.

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3 0
3 years ago
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Answer:

1,2. 6.0

Step-by-step explanation:

That is the answer

5 0
3 years ago
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