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storchak [24]
2 years ago
13

A cone has a slant length of 5 and a diameter of 4. What is the volume of the cone? Use π ≈ 3.14.

Mathematics
2 answers:
Olegator [25]2 years ago
3 0

Answer:

V = 19.19 cubic units

None of the options are correct.

Step-by-step explanation:

Volume of a cone is given as;

V = ⅓πr²h

Now, we are given;

diameter = 4 units

Thus radius;r = diameter/2 = 4/2 = 2 units

I have attached an image to show the diagram of the cone.

Now, to find the height (h), we know the radius(r) and we know the slant length(l) . So we can use Pythagoras theorem to find the height.

From Pythagoras theorem;

r² + h² = l²

Where l is the hypotenuse or the slant side while "r" is the radius of the cone while the height will be "h"

Thus;

2² + h² = 5²

h² = 5² - 2²

h² = 25 - 4

h² = 21

h = √21

h = 4.5826 units

So height (h) = 4.5826 units

Volume of cone;V = ⅓πr²h

We are told that π = 3.14

Thus;

V = ⅓ x 3.14 x 2² x 4.5826

V = 19.19 cubic units

Gennadij [26K]2 years ago
3 0

Answer:A on edge

Step-by-step explanation:

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tatyana61 [14]

Annually:    Total Amount= $1,611.76   Interest Amount= $711.76

Semiannually: Total Amount= $1,625.50  Interest Amount= $725.50

Quarterly:  Total Amount= $1,632.62   Interest Amount= $732.62

7 0
2 years ago
Read 2 more answers
ou have two parents, four grandparents, eight great-grandparents, and so forth. (a) If all your ancestors were distinct, what wo
Maslowich

Answer:

Part A:

2^{40}-2\\=1.0995*10^{12} ancestors

Part B:

Generations Age=25*39=975 years

Part C:

  1. Some ancestors on different branches of the family tree must be the same.
  2. There could not have been 39 generations in my line of ancestry.

Step-by-step explanation:

Given Data:

Two Parents, Four Grand Parents, Eight great Grand Parents.

Generation=39

Solution:

Part A:

From given data Following series is made:

2+2^2+2^3+.........+2^{39}

Now, Above series will become:

2[1+2+2^2+......+2^{38}]

From geometric Sequence:

2[\frac{2^{38+1}-1}{2-1} ]

2^{40}-2\\=1.0995*10^{12} ancestors

Part B:

Generations Age=years*Number of generations

Generations Age=25*39=975 years

Part C:

Number of people lived= 10^11

Ancestors=1.0995*10^{12} ancestors

10^{11}

It means ancestors are not distinct, it means:

  1. Some ancestors on different branches of the family tree must be the same.
  2. There could not have been 39 generations in my line of ancestry.
5 0
2 years ago
Allowance $10<br> Earn $18<br> Spend $3.28, $7.15, and $9.54<br> Save?
julsineya [31]

Answer:

8.03

Step-by-step explanation:

10+18 = 28

28 - 3.28 - 7.15 - 9.54 = 8.03

4 0
2 years ago
Which table of values could be generated by the equation 10x + 5y = 15?
Ad libitum [116K]
Write the given equation AS FOLLOWS:
10x + 5y = 15
5y = 15 - 10x
Divide through by 5.
y = 3 - 2x

Test  x=0:  y = 3 - 2*0 = 3  =>  (0,3)     Correct for B
Test  x=1:.  y = 3 - 2*1 = 1    => (1,1)        Correct for B
Test x=2:   y = 3 - 2*2 = -1  => (2,-1)     Correct for B

Answer:  B

3 0
2 years ago
What is the area of the base of the cone below?
frutty [35]

<u>Given</u>:

Given that the height of the cone is 12 ft.

The volume of the cone is 90 ft³

We need to determine the area of the base of the cone.

<u>Area of the base of the cone:</u>

The area of the base of the cone can be determined using the formula,

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

where the base area is A=\pi r^2

Substituting the value of A in the above formula, we get,

V=\frac{1}{3}A h

Substituting V = 90 and h = 12, we get;

90=\frac{1}{3}A (12)

90=4A

Dividing both sides by 4, we get;

22.5 =A

Thus, the area of the base of the cone is 22.5 square feet.

Hence, Option c is the correct answer.

8 0
2 years ago
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