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2 years ago

What is the volume of this prism?

Mathematics

1 answer:

Mandarinka [93]2 years ago

8 0

Answer:

144 cm^3

Step-by-step explanation:

The formula for the volume of a rectangular prism is <em>l x w x h. </em>

Here, the length is 4, the width is 4, and the height is 4.

4 x 4 x 9 =

16 x 9 =

144 cm^3

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Gravel is being dumped from a conveyor belt at a rate of 20 ft3/min, and its coarseness is such that it forms a pile in the shap

11Alexandr11 [23.1K]

Answer:

0.25 feet per minute

Step-by-step explanation:

Gravel is being dumped from a conveyor belt at a rate of 20 ft3/min. Since we are told that the shape formed is a cone, the rate of change of the volume of the cone.

$\dfrac{dV}{dt}=20$ ft^3/min$

$\text{Volume of a cone}=\dfrac{1}{3}\pi r^2 h$

Since base diameter = Height of the Cone

Radius of the Cone = h/2

Therefore,

$\text{Volume of the cone}=\dfrac{\pi h}{3} (\dfrac{h}{2}) ^2 \\V=\dfrac{\pi h^3}{12}$

$\text{Rate of Change of the Volume}, \dfrac{dV}{dt}=\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}$

Therefore: $\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}=20$

We want to determine how fast is the height of the pile is increasing when the pile is 10 feet high.

$h=10$ feet$\\\\\dfrac{3\pi *10^2}{12}\dfrac{dh}{dt}=20\\25\pi \dfrac{dh}{dt}=20\\ \dfrac{dh}{dt}= \dfrac{20}{25\pi}\\ \dfrac{dh}{dt}=0.25$ feet per minute (to two decimal places.)$

When the pile is 10 feet high, the height of the pile is increasing at a rate of 0.25 feet per minute

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3 years ago

Solve systems using substitution PLEASE

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X=5. y=35.

To solve, substitute the 7x into the equation for y. Solve. You get x=5. Then put that into your first equation. Solve. You get y=35. Hope that helps!!

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2 years ago

What is the final cost of your $15 umbrella with 6% tax?

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Step-by-step explanation:

15 × 6/100=0.9

15+0.9=$15.9

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3 years ago

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