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2 years ago

Find the dimensions of the right circular cylinder of maximum volume that can be placed inside of a sphere of radius R.

Mathematics

1 answer:

Evgen [1.6K]2 years ago

3 0

This question is incomplete, the complete question is;

Find the dimensions of the right circular cylinder of maximum volume that can be placed inside of a sphere of radius R(10cm)

What is the maximum volume?

Answer:

a) Dimensions of the cylinder are; Radius = 8.1650 cm , Height = 11.547 cm

b) the maximum volume is 2418 cm³

Step-by-step explanation:

From the image

radius of the sphere is 10cm

radius of the cylinder is x and its height is 2y

The volume of cylinder is V = πr²h = πx²(2y)

Get V as function of just one variable x² + y² = 100

x² = 100 - y²

Therefore V = π( 100-y² )(2y) = 200πy-2πy³

V will be a maximum when V' = 0

V' = 200π - 6πy² =0

y² = 200π / 6π = 100/3

y = √(100/3) = 5.7735

x² = 100 - y²

x² =100 - (100/3)

x = √(200/3)

x = 8.1650

So The maximum volume will occur when the radius is 8.1650 cm

and the height 2y is 2(5.7735) = 11.547 cm

The maximum volume is

πr²h = π(8.1650)² (11.547 )

= 2418 cm³

Therefore the maximum volume is 2418 cm³

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One number is ten times another number. Their sum is 253.

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Answer:

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Step-by-step explanation:

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2 years ago

Simplify tan9x-tan5x / 1+tan9xtan5x

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Answer:

The given expressions simplifies to tan (4x).

Step-by-step explanation:

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By TRIGONOMETRIC IDENTITY:

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Putting this identity here, and taking A = 9 x, B = 5 x, we get

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2 years ago

In the diagram, what is mAngleVSR?

katovenus [111]

The mAngleVSR m Angle VSR is mathematically given as

$\theta$ = 80°

This is further explained below.

<h3>What is mAngleVSR?</h3>

Generally, Draw two lines: one that connects the points R, S, and U, and another that connects the points V, S, and T. (see attached diagram). At point S, these lines come together to create four angles, which are denoted by the letters RSV, VSU, UST, and TSR respectively.

The angles VSU and RST are both considered to be vertical angles, as are the angles RSV and UST. Vertical angles are equivalent, therefore

m∠VSU = m∠RST = 100°

m∠RSV = m∠UST

In conclusion, Angles RSV and VSU are considered supplementary angles since their sum is equal to 180 degrees. Som

m∠RSV = 180° - m∠VSU =180° - 100° = 80°

Angle RSV is the same as angle VSR (the name of the angle may be read either from the right to the left or from the left to the right).