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lesya [120]
3 years ago
7

The radius of a sphere is increasing at a rate of 3 mm/s. how fast is the volume of the sphere increasing when the diameter is 1

0 mm?
Mathematics
1 answer:
vredina [299]3 years ago
5 0

We will find the rate of change of volume with respect to the change of radius.


Volume, V(r) = (4/3) π r^3


Find rate of change of volume with respect to change of radius by differentiation


V'(r)=dV/dr = d[(4/3) π r^3]/dr = (4/3) π d[r^3]/dr =(4/3) π 3r^2


Therefore when diameter=10mm, r=5mm


V'(r)=V'(5)=(4/3) π (3(5^2))=(4/3) π 75 = 100 π mm^3/mm

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A cone has a 4 radius and a 8 height what is the volume
Marta_Voda [28]

Hey there! I'm happy to help!

To find the volume of a cone, you multiply the base by the height and then divide by three.

First, we need to find the base. A cone has a circle for the base. To find the area of a circle, we square the radius and multiply it by pi (we will use 3.14).

4²=16

16×3.14= 50.24

Now, we multiply our base by the height.

50.24×8=401.92

Finally, we divide by three.

401.92÷3≈133.973 (to nearest thousandth)

Therefore, the volume of the cone is about 133.973 units cubed. If you were to use exact pi, it would be more like 134 because of all those decimals after pi!

Now you can find the volume of cones!

I hope that this helps! Have a wonderful day!

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In the storage room of a certain bakery, the ratio of sugar to flour is 5 to 8, and the ratio of flour to baking soda is 10 to 1
olasank [31]

Answer:

1,500

Step-by-step explanation:

Ratio of Sugar to Flour: 5:8 -> 25:40

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Sugar to Flour to Soda: 25x:40x:4x

\frac{40x}{(4x+60)} = \frac{8}{1} -> x = 60

Sugar = 25x = 1,500

Hope this helps :)

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Step-by-step explanation:


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Answer:

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Step-by-step explanation:

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