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3 years ago

15

Determine whether the statement is true or false, and explain why.

1 answer:

ipn [44]3 years ago

5 0

Answer:

False

Step-by-step explanation:

The statement is False, because the average value of a funciton f(x) on an interval is given by the value of the integral of the function on that interval divided by its length. In this case, the integral is right, but we are not integrating exactly f, and thats why the average value is not given correctly.

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.5

Step-by-step explanation:

.5

yellow= .30

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green= .10

red- .10

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Algebra- systems of equations (x,y)<br> 3x + 4y = 56<br> x = 3y + 12

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3 years ago

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Find the amount of empty space within a cylinder containing three solid spheres, where each sphere has a radius of 3 cm. (Volume

aalyn [17]

Answer : The correct option is, (A) $54\pi cm^3$

Step-by-step explanation :

First we have to calculate the volume of cylinder.

Formula used:

Volume of cylinder = $\pi r^2h$

where,

r = radius = 3 cm

h = height = 18 cm (We are assuming that 3 solid spheres stacked to each other = 3 × diameter of each sphere = 3 × 2 × 3 = 18)

Volume of cylinder = $\pi (3cm)^2\times (18cm)$

Volume of cylinder = $162\pi cm^3$

Now we have to calculate the volume of 3 solid spheres.

Formula used:

Volume of 3 spheres = $3\times \frac{4}{3}\pi r^3$

Volume of 3 spheres = $4\pi r^3$

Volume of 3 spheres = $4\pi (3)^3$

Volume of 3 spheres = $108\pi cm^3$

Now we have to calculate the amount of empty space within a cylinder.

Amount of empty space within a cylinder = Volume of cylinder - Volume of 3 spheres

Amount of empty space within a cylinder = $162\pi cm^3-108\pi cm^3$

Amount of empty space within a cylinder = $54\pi cm^3$

Therefore, the amount of empty space within a cylinder is, $54\pi cm^3$

5 0

3 years ago