How to find R of a cone?

2 answers:

6 0

If you are given the volume then
V=(1/3)hpir^2
h=height
r=radius
V=volume
solve for r

times 3 both sides
3V=hpir^2
dvivide both sides by hpi
$\frac{3V}{h \pi}=r^2$
sqrt both sides
$\sqrt{\frac{3V}{h \pi}} =r$

bonufazy [111]3 years ago

4 0

Multiply the volume by 3.
Multiply the height by π, which is a numeric constant that begins 3.14 and never terminates.
Divide the tripled volume by the product of the height and π.
Find the square root of the result from the 3rd step

hope this helped:)

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The radius of a sphere is increasing at a rate of 5 mm/s. How fast is the volume increasing (in mm3/s) when the diameter is 40 m

jeka94

9514 1404 393

Answer:

8000π mm^3/s ≈ 25,133 mm^3/s

Step-by-step explanation:

The rate of change of volume is found by differentiating the volume formula with respect to time.

V = 4/3πr^3

V' = 4πr^2·r'

For the given numbers, this is ...

V' = 4π(20 mm)^2·(5 mm/s) = 8000π mm^3/s ≈ 25,133 mm^3/s

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Additional comment

By comparing the derivative to the area formula for a sphere, you see that the rate of change of volume is the product of the area and the rate of change of radius. This sort of relationship will be seen for a number of different shapes.

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