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Fantom [35]
3 years ago
15

How to find Surface Area & Volume of Cylinder??? please help......

Mathematics
2 answers:
AlladinOne [14]3 years ago
7 0

Answer:

A cylinder's volume is π r² h, and its surface area is 2π r h + 2π r².

m_a_m_a [10]3 years ago
4 0

Step-by-step explanation:

The volume of a cylinder=πr²h

The surface area of the cylinder = 2πr(r+h)

where, r = radius of the cylinder

and h= height of the cylinder

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Find the surface area of the part of the circular paraboloid z=x^2+y^2 that lies inside the cylinder X^2+y^2=1
hichkok12 [17]

Answer:

\mathbf{\dfrac{\pi}{6}[5 \sqrt{5}-1]}

Step-by-step explanation:

Given that:

The surface area (S.A) z = x^2 +y^2

Hence the S.A is of form z = f(x,y)

Then the S.A can be represented with the equation

A(S) = \iint _D \sqrt{1+ (\dfrac{\partial z}{\partial x})^2+ (\dfrac{\partial z}{\partial y})^2} \ dA

where :

D = cylinder x^2 +y^2 =1

In polar co-ordinates:

D = {(r, θ): 0≤ r ≤ 1, 0 ≤ θ ≤ 2π)

Similarly, \dfrac{\partial z}{\partial x} = 2x and \dfrac{\partial z}{\partial y} = 2y

Therefore;

S.A = \iint_D \sqrt{1+4x^2+4y^2} \ dA

= \iint_D \sqrt{1+4(x^2+y^2)} \ dA

= \int^{2 \pi}_{0} \int^{1}_{0}  \sqrt{1+4r^2} \ r \ dr \d \theta

= [\theta]^{2 \pi}_{0} \dfrac{1}{8}\times \dfrac{2}{3}\begin {bmatrix} (1+4r^2)^{\dfrac{3}{2}}\end {bmatrix}^1_0

= 2 \pi \times \dfrac{1}{12}[5^{\dfrac{3}{2}} - 1]

\mathbf{=\dfrac{\pi}{6}[5 \sqrt{5}-1]}

6 0
3 years ago
X^2 -50x+456=0 solve this algebraiclly find x
bagirrra123 [75]

Answer:

x=-406

Step-by-step explanation:

x^2-50x+456=0

x^2-50x=-456

This is because we subtract 456 from each side.

x-50=-456

We then divide the whole equation by <em>x</em> .

x=-406

Adding 50 to both sides gives us <em>x</em> by itself, hope this helps :D

8 0
2 years ago
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HELP: Will Award Brainliest! Simplify 17x - 12 = 114 + 3x
mrs_skeptik [129]

Answer:

x=9

Step-by-step explanation:

17x - 12 = 114 + 3x

First  Subtract 3x from both sides

14x - 12 = 114

Add 12 to both sides

14x=126

Divide by GCF (14)

x=9

Hope this helps! Plz award Brainliest : )

5 0
3 years ago
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The vertex of the graph of f(x) = |x - 3| +6 is located at<br> Done<br> Intro
Igoryamba

Answer:

The vertex of the graph is located at the point (3,6)

Step-by-step explanation:

Here, we want to know where the vertex of the equation if plotted will be

To get this, what we have to do is to equate the expression that we have in the absolute value to zero

After this, we then proceed to solve for the value of x

We have this as;

x -3 = 0

hence;

x = 0 + 3

x = 3

to get the y-value of the vertex, we look at the value at the side of the absolute value

This value is 6 and thus, the y-value of the vertex point is 6

So the coordinates of the vertex is (3,6)

8 0
3 years ago
The shirt costs twice as much as the shoes. Together, they cost more than $200. What is the minimum cost for each item? (Round t
miskamm [114]
$200 because you can't round toe the nearest dollar

4 0
3 years ago
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