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IgorC [24]
3 years ago
9

Cylinder A has a radius of 10 inches and a height of 5 inches. Cylinder B has a volume of 750π. What is the percentage change in

volume from cylinder A to cylinder B?
Mathematics
2 answers:
Firlakuza [10]3 years ago
6 0

Answer:

50% change in volume

Step-by-step explanation:

<h2>This problem bothers on the mensuration of solid shapes.</h2>

In this problem we are to find the volume of the first  cylinder and compare with the second cylinder.

Given data

Volume v =  ?

Diameter d= ?

Radius r =  10 in

Height h=  5 in

we know that the volume of a cylinder is expressed as

volume = \pi r^{2}h

Substituting our given data we have

volume = \pi*10^{2}*5\\ volume= \pi *100*5\\volume= 500\pi in^{3} \\

The first cylinder as a volume of 500\pi

The change in volume is 750\pi - 500\pi = 250\pi

percentage = \frac{250\pi }{500\pi } *100

percentage=0.5*100= 50%

Kobotan [32]3 years ago
4 0

Answer:

50% increase

Step-by-step explanation:

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2 years ago
A car is being driven at a rate of 40 ft/sec when the brakes are applied. The car decelerates at a constant rate of 10 ft/sec2.
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Answer:

80 feet

Step-by-step explanation:

Given:

Initial speed of the car (v_0) = 40 ft/sec

Deceleration of the car (\frac{dv}{dt}) = -10 ft/sec²

Final speed of the car (v_x) = 0 ft/sec

Let the distance traveled by the car be 'x' at any time 't'. Let 'v' be the velocity at any time 't'.

Now, deceleration means rate of decrease of velocity.

So, \frac{dv}{dt}=-10\ ft/sec^2

Negative sign means the velocity is decreasing with time.

Now, \frac{dv}{dt}=\frac{dv}{dx}(\frac{dx}{dt}) using chain rule of differentiation. Therefore,

\frac{dv}{dx}\cdot\frac{dx}{dt}= -10\\\\But\ \frac{dx}{dt}=v.\ So,\\\\v\frac{dv}{dx}=-10\\\\vdv=-10dx

Integrating both sides under the limit 40 to 0 for 'v' and 0 to 'x' for 'x'. This gives,

\int\limits^0_{40} {v} \, dv=\int\limits^x_0 {-10} \, dx\\\\\left [ \frac{v^2}{2} \right ]_{40}^{0}=-10x\\\\-10x=\frac{0}{2}-\frac{1600}{2}\\\\10x=800\\\\x=\frac{800}{10}=80\ ft

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3 years ago
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