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3 years ago

The radius of a cone is 5 and the height is 11. What is the slant height, lateral area, total area and volume of the cone

Mathematics

1 answer:

sukhopar [10]3 years ago

8 0

Answer:

Slant height = 12.083

Volume = 287.98

Step-by-step explanation:

To find the slant height, we just need to use the Pythagorean Theorem.

a² + b² = c²

a = 5

b = 11

5² + 11² = c²

25 + 121 = c²

146 = c²

Root both sides to find c

√146 = √c²

c = 12.083

To find the volume we need to use this formula: πr²h/3

r = radius (5)

h = hieght (11)

π · 5² · 11 ÷ 3 = 287.98

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Crazy boy [7]

Hi there!

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I believe your answer is:

$x = \frac{1}{4}$

»»————-　★　————-««

Here’s why:

⸻⸻⸻⸻

$\boxed{\text{Solving the equation for x...}}\\\\4x + 54 = 55\\----------\\\rightarrow 4x + 54 - 54 = 55 - 54\\\\\rightarrow 4x = 1\\\\\rightarrow \frac{4x=1}{4}\\\\\rightarrow \boxed{x=\frac{1}{4}}$

⸻⸻⸻⸻

»»————-　★　————-««

Hope this helps you. I apologize if it’s incorrect.

6 0

3 years ago

Read 2 more answers

How do I determine z ∈ C:

saw5 [17]

Simplify the coefficient of z on the left side. We do this by rationalizing the denominators and multiplying them by their complex conjugates:

$\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{3-2i}{1+i}\cdot\dfrac{1-i}{1-i} - \dfrac{5+3i}{1+2i}\cdot\dfrac{1-2i}{1-2i}$

$\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{(3-2i)(1-i)}{1-i^2} - \dfrac{(5+3i)(1-2i)}{1-(2i)^2}$

$\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{3 - 2i - 3i + 2i^2}{1-(-1)} - \dfrac{5 + 3i - 10i - 6i^2}{1-4(-1)}$

$\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{3 - 5i + 2(-1)}2 - \dfrac{5 - 7i - 6(-1)}5$

$\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{1 - 5i}2 - \dfrac{11 - 7i}5$

$\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{1 - 5i}2\cdot\dfrac55 - \dfrac{11 - 7i}5\cdot\dfrac22$

$\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{5 - 25i - 22 + 14i}{10}$

$\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = -\dfrac{17 + 11i}{10}$

So, the equation is simplified to

$-\dfrac{17+11i}{10} z = \dfrac12 - \dfrac{2i}5$

Let's combine the fractions on the right side:

$\dfrac12 - \dfrac{2i}5 = \dfrac12\cdot\dfrac55 - \dfrac{2i}5\cdot\dfrac22$

$\dfrac12 - \dfrac{2i}5 = \dfrac{5-4i}{10}$

Then

$-\dfrac{17+11i}{10} z = \dfrac{5-4i}{10}$

reduces to

$-(17+11i) z = 5-4i$

Multiply both sides by -1/(17 + 11i) :

$\dfrac{-(17+11i)}{-(17+11i)} z = \dfrac{5-4i}{-(17+11i)}$

$z = -\dfrac{5-4i}{17+11i}$

Finally, simplify the right side:

$-\dfrac{5-4i}{17+11i} = -\dfrac{5-4i}{17+11i} \cdot \dfrac{17-11i}{17-11i}$

$-\dfrac{5-4i}{17+11i} = -\dfrac{(5-4i)(17-11i)}{17^2-(11i)^2}$

$-\dfrac{5-4i}{17+11i} = -\dfrac{85 - 68i - 55i + 44i^2}{289-121(-1)}$

$-\dfrac{5-4i}{17+11i} = -\dfrac{85 - 68i - 55i + 44(-1)}{410}$

$-\dfrac{5-4i}{17+11i} = -\dfrac{41 - 123i}{410}$

$-\dfrac{5-4i}{17+11i} = -\dfrac{41 - 41\cdot3i}{410}$

$-\dfrac{5-4i}{17+11i} = -\dfrac{1 - 3i}{10}$

So, the solution to the equation is

$z = -\dfrac{1-3i}{10} = \boxed{-\dfrac1{10} + \dfrac3{10}i}$

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What is the perimeter of rectangle JKUM?<br> 32 units<br> 44 units<br> 56 units

yKpoI14uk [10]

Answer:

Step-by-step explanation:

8 0

4 years ago

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A fruit stand has 200 apples. They order 19 bags with 12 apple each. They sell 42 bags that have 8 apples each. The owner says t

Sunny_sXe [5.5K]

Your best answer is C.

Round up 19 bags they ordered to 20, then multiply by 12 to get 240 apples they ordered.

Round down the 42 to 40. 40 x 8 = 320 apples sold.

200 to start + 240 ordered = 440 apples
440-320 = 120

5 0

3 years ago