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Tanya [424]
3 years ago
15

Find the volume of a right circular cone that has a height of 18.9 in and a base with a

Mathematics
1 answer:
Dmitriy789 [7]3 years ago
3 0

Answer:

The volume of the cone is:

  • <u>112.6 cubic inches.</u>

Step-by-step explanation:

You should know that the volume of a straight circular cone is equal to:

  • Cone volume = (1/3) PI * r ^ 2 * h

Where:

<em>r = radius. </em>

<em>h = height. </em>

Since the radius and diameter are not provided in the exercise but the circumference, the circumference formula should be used and the diameter must be cleared:

  • Circumference = PI * Diameter.

When clearing you get:

  • Diameter = circumference / PI

By replacing the data you get:

  • Diameter = 15 inches / PI
  • Diameter = 4.77 inches.

Since the radius is equal to half the diameter, then the diameter is equal to 2,385 inches, now having the value of radius we proceed to replace in the volume formula:

  • Cone volume = (1/3) PI * 2.385 in^2 * 18.9 in
  • Cone volume = 112.581541 in^3
  • <u>Cone volume = 112.6 in^3</u>
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Scott wants to buy fencing to place around a semicircular rock garden The diameter of the semicircle is 16 feet Using 3.14 for p
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The diameter of the semicircle is 16 feet.

He calculates that he needs to buy abut 25.12 feet of fencing.

To find amount of fencing we find the circumference of semicircle

Circumference of semicircle = \frac{1}{2}\pi d+d

Where d is the diameter of the circle

d= 16 given and value of pi is 3.14

Circumference of semicircle = \frac{1}{2}*3.14*16+16

=25.12 + 16 = 41.12 feet

Scott's calculation was wrong because he forgot to add the diameter d

Circumference of circle  is half way of circle plus the diameter of circle.

Correct amount of fencing = 41.12 feet



7 0
3 years ago
Which of the following statements is correct? A. During times of high inflation, interest rates on new loans for cars, homes, an
svet-max [94.6K]

Answer:

D.

Step-by-step explanation:

The longer the interest rate, the more money it will generally cost someone.

8 0
3 years ago
First, I add 1. Then, I multiply by 2. Next, I divide by 3. As a result, I get 4. What is my starting number?
Ira Lisetskai [31]

Answer:5

Step-by-step explanation:

reverse the steps

2(x+1)/3=4

2(x+1)/3×3=4×3

2(x+1)/2=12/2

x+1=6

x=6-1

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6 0
3 years ago
Read 2 more answers
What is the quotient of 12 and the opposite of 3 plus the product of the opposite of 14 and 4
oee [108]
(12/-3)+(-14*4)
(-4)+(-56)
[-60]

-- i dont understand what you mean by "opposite of" so i assumed you meant negative??
6 0
3 years ago
A certain car rental location charges a daily fee as well as a mileage charge. On one trip a businessman rented a car for the da
nikklg [1K]

Answer:

x\approx 267\ miles

Step-by-step explanation:

<u>Linear Modeling</u>

Some events can be modeled as linear functions. If we are in a situation where a linear model is suitable, then we need two sample points to make the model and predict unknown behaviors.

The linear function can be expressed in the slope-intercept format:

f(x)=mx+b

For the problem at hand, we must pick the adequate variables according to the data provided.

The question states the charge for renting a car is a function of the mileage. It also provides two points from which we can build our model. Let's set the following variables:

c = the charge for renting a car in dollars

x = the distance driven by the businessman in miles

Representing the ordered pair as (x,c), we have the points: (150,79) and (65,63.70). Our model will be expressed as:

c = mx+b

We must find the values of m and b with the data provided. Substituting the first point:

79 = 150m+b

Substituting the second point:

63.70 = 65m+b

Both equations form the following system:

\left\{\begin{matrix}150m+b=79\\ 65m+b=63.70 \end{matrix}\right.

Subtracting both equations:

150m-65m=79-63.70

Note the variable b was canceled out in the operation, leaving only the variable m to solve. Joining like terms:

85m=15.3

Solving:

m=15.3/85=0.18

From the first equation

79 = 150m+b

Solving for b:

b=79-150m=79-150(0.18) = 52.

The model for the problem is:

c=0.18x+52

Now we need to calculate how many miles (x) could be driven for c=$100. From the equation above, substitute c=100

100=0.18x+52

Solve for x:

0.18x+52=100

0.18x=100-52=48

x=48/0.18=266.67

Rounding to the closest integer:

\boxed{x\approx 267\ miles}

7 0
3 years ago
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