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MrMuchimi
3 years ago
8

Suppose the circumference of a circle is 15pi. What is its diameter?

Mathematics
1 answer:
IRISSAK [1]3 years ago
7 0
The circumference of a circle is proportional to its diameter.

C\propto d\\ \\ \therefore \quad C=kd

Now, when d=1, C=π, therefore:

k=π

This means that:

C=\pi d

If C=15π:

15π=πd

Therefore:

d=15
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Answer:

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inner radius = 10/2 = 5 in

outer radius = 5 + a

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V = 4/3 π (4+a)³ - 4/3 π4³

V = 4/3 π ( 4³ + 12a² + 48a + a³ -4³)

V = 4/3 π(a³ + 12a² + 48a)

dV/dt = 4/3 π (3a²da/dt + 24ada/dt + 48da/dt)

dV/dt = 4π(a²da/dt + 8ada/dt + 16da/dt)..............(1)

When a = 3 in, dV/dt = -15 m³/min

Substitute these values into equation (1)

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-15/4π = 49da/dt

-1.194 = 49da/dt

da/dt = -1.194/49

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The area of a sphere, A = 4πr²

The outer surface area of the sphere, A = 4π(4+a)²

dA/da = 8π (4+a) da/dt

a = 3 in, da/dt = -0.024 in/min

dA/da = 8π(4+3)*(-0.024)

dA/da = -4.22 in²/min

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