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slavikrds [6]
2 years ago
5

A cylinder has a volume of 175 cubic units and a height of 7 units. The diameter of the cylinder is

Mathematics
2 answers:
olga nikolaevna [1]2 years ago
5 0
Easy the answer is... about 5
postnew [5]2 years ago
5 0

Answer: 5.64 units

Step-by-step explanation:

The volume of a cylinder is given by :-

\text{Volume}=\pi r^2 h, where r is radius and h is height of the cylinder.

Given : Volume of cylinder = 175 cubic units

Height = 7 units.

Substitute these values in the above formula , we have

175=(3.14) r^2 (7)\\\\\Rightarrow\ r^2=\dfrac{175}{(3.14)(7)}\\\\\Rightarrow\ r^=7.96178343949\\\\\Rightarrow\ r\approx2.82

Now, the diameter of the cylinder will be given by :-

d=2(2.82)=5.64\text{ units}

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Let's think about the information in the problem. The problem tells us a few key points:

  • The number of rabbits grows exponentially
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Since we know we are going to be working with an exponential model, we can start with a base exponential model:

a = P \cdot r^t

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Based on the information in the problem, we can create two equations:

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The first equation tells us that P = 20, or that we start with 20 rabbits.  Thus, we can change the second equation to:

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Now, we don't know r, but we want to, so let's solve for it.

5 = r^6

r = \sqrt[6]{5}


Now, the problem is asking us how many rabbits we are going to have after one year (t = 12), so let's find that:

a = 20 \cdot (\sqrt[6]{5})^{12}

a = 20 \cdot (5^{\frac{1}{6}})^{12}

a = 20 \cdot 5^2

a = 500


After one year, we will have 500 rabbits.


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