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Olenka [21]
3 years ago
7

The cylinder and the sphere below have the same radius and the same volume. What is the height of the cylinder?

Mathematics
1 answer:
lyudmila [28]3 years ago
4 0

Answer:

Height of cylinder (h) = (4/3)R

Step-by-step explanation:

Given:

Radius of cylinder (r1) = R

Height of cylinder (h) = H

Radius of sphere (r2) = R

Volume of cylinder = volume of sphere

Find:

Height of cylinder (h) = H = ?

Computation:

Volume\ of\ cylinder = volume\ of\ sphere\\\\ \pi (r1)^2h =\frac{4}{3} \pi (r2)^3\\\\\pi (R)^2h =\frac{4}{3} \pi (R)^3\\\\ h=\frac{4}{3}  (R)

Height of cylinder (h) = (4/3)R

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Answer:

-1/4

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3 years ago
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"A 12​-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the pavement directly away from t
Svet_ta [14]

Answer:

Step-by-step explanation:

The question has typographical errors. The correct question is:

"A 12​-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the pavement directly away from the building at 3 ​feet/second, how fast is the top of the ladder moving down when the foot of the ladder is 5 feet from the​ wall?

Solution:

The ladder forms a right angle triangle with the ground. The length of the ladder represents the hypotenuse.

Let x represent the distance from the top of the ladder to the ground(opposite side)

Let y represent the distance from the foot of the ladder to the base of the wall(adjacent side)

The bottom of the ladder is sliding along the pavement directly away from the building at 3ft/sec. This means that y is increasing at the rate of 3ft/sec. Therefore,

dy/dt = 3 ft/s

The rate at which x is reducing would be

dx/dt

Applying Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side², it becomes

x² + y² = 12²- - - - - - - -1

Differentiating with respect to time, it becomes

2xdx/dt + 2ydy/dt = 0

2xdx/dt = - 2ydy/dt

Dividing through by 2x, it becomes

dx/dt = - y/x ×dy/dt- - - - - - - - - - 2

Substituting y = 5 into equation 1, it becomes

x² + 5 = 144

x² = 144 - 25 = 119

x = √119 = 10.91

Substituting x = 10.91, dy/dt = 3 and y = 5 into equation 2, it becomes

dx/dt = - 5/10.91 × 3

dx/dt = - 1.37 ft/s

7 0
3 years ago
I need a specific explanation of how to answer this
zimovet [89]
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you can check them with FOIL.
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Morgan has 1/3 of a pond of bottle caps storend evenly in 3 boxes. How many pounds of bottles caps are in each box?
GREYUIT [131]
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3 years ago
The length of a radius of a circle, measured in centimeters, is represented by the expression x + 1.5. The diameter of the circl
Tomtit [17]

The value of x of a circle with radius x + 1.5 and diameter of 9 2 / 5 cm is 7.9 cm

<h3>Radius of a circle</h3>

Radius of a circle is half of the diameter of a circle. The radius extend from the centre of the circle to the circumference.

Mathematically,

radius = 1 / 2 (diameter)

Therefore,

radius = (x + 1.5) cm

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Therefore,

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learn more on radius here: brainly.com/question/12183018

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