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3 years ago

The height of a cylinder is four times its radius. Find a function that models the volume V of the cylinder in terms of its radi

us r.

Mathematics

1 answer:

sammy [17]3 years ago

7 0

$V=\pi r^2H\\\\H=4r\\\\then:\\\\V(r)=\pi r^2(4r)=4\pi r^3$

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For what value of b do the lines bx+3y=10 and x–2y=4 intersect at a point on the x-axis?

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3 years ago

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2 years ago

A conical paper cup is 10 cm tall with a radius of 10 cm. The cup is being filled with water so that the water level rises at a

Alborosie

Answer:

Water is being pored in the cone with the rate of 401.92 cm³ per second.

Step-by-step explanation:

There is a cone having height h = 10 cm and radius r = 10 cm

That means h = r

Rate of change of water level $\frac{dh}{dt}=2$ cm per second

Since volume of a cone is represented by the formula,

$V=\frac{1}{3}\pi r^{2}h$

Now we have to find the value of $\frac{dV}{dt}$ .

$\frac{dV}{dt}=\frac{d}{dt}(\frac{1}{3}\pi r^{2}h)$

Since r = h

$\frac{dV}{dt}=\frac{d}{dt}(\frac{1}{3}\pi h^{3} )$

$\frac{dV}{dt}=\frac{3}{3}\pi h^{2}.\frac{dh}{dt}$

For h = 8 cm and $\frac{dh}{dt}=2$ cm per second.

$\frac{dV}{dt}=\frac{3}{3}\pi (8)^{2}\times (2)$

$\frac{dV}{dt}=128\pi$ = 401.92 cubic cm per second

Therefore, water is being pored with the rate of 401.92 cm³ per sec.

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3 years ago