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Aloiza [94]
3 years ago
14

The height of a cylinder is 9.5 centimeters. the diameter of this cylinder is 1.5 centimeters longer than the height. which is c

losest to the volume of the cylinder?
Mathematics
1 answer:
Llana [10]3 years ago
6 0
Given that t<span>he height of a cylinder is 9.5 centimeters and that the diameter of this cylinder is 1.5 centimeters longer than the height, thus, the diameter of the cylinder is 9.5 + 1.5 = 11 cm and the radius of the cylinder is diameter / 2 = 11 / 2 = 5.5 cm.

The volume of the cylinder is given by

</span>V=\pi r^2h \\  \\ =\pi(5.5)^2(9.5) \\  \\ =\pi(30.25)(9.5) \\  \\ =287.375\pi\approx902.8cm^3<span>
</span>
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Answer:

5P3*6C4=60*15=900

Step-by-step explanation:

5P3 refers to the permutations of 5 items taken 3 at a time. To evaluate this, we use factorials as follows;

5P3=\frac{5!}{(5-3)!}

The factorial of an integer n is evaluated as;

n!=n*(n-1)*(n-2)*(n-3).......3*2*1

Using this concept, the above expression can now be simplified as follows;

5P3=\frac{5!}{2!}=\frac{5*4*3*2!}{2!}=5*4*3=60

Therefore, the permutations of 5 items taken 3 at a time is 60.

The next expression, 6C4 refers to the combinations of 6 items taken 4 at a time. The simplification utilizes similar concepts of permutations since we shall be involving factorials;

6C4=\frac{6!}{4!(6-4)!}=\frac{6!}{4!*2!}=\frac{6*5*4!}{4!*2*1}=\frac{6*5}{2*1}=15

Therefore, the combinations of 6 items taken 4 at a time is 15.

The final step is to evaluate the product;

5P3*6C4=60*15=900

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Step-by-step explanation:

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Multiplying equation (2) with 5 and subtracting from equation (1):

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