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Airida [17]
3 years ago
5

Consider this sphere inside the cylinder. Which statements are true? Check all that apply. NEED HELP ASAP​

Mathematics
2 answers:
-Dominant- [34]3 years ago
6 0

Option A: The height of the cylinder is equal to the diameter of the sphere.

Option C: The radius of the sphere is half the height of the cylinder.

Option E: The volume of the sphere is two-thirds the volume of the cylinder.

Solution:

The sphere is inside the cylinder.

Let r be the radius of the sphere.

Option A: The height of the cylinder is equal to the diameter of the sphere.

The sphere is fully occupied the cylinder.

If we draw the vertical line through enter of the sphere, which is equal to the height of cylinder.That is h = d. It is true.

Option B: The height of the cylinder is two times the diameter of the sphere.

That is h = 2d. From the above option, we know that h = d.

So, it is not true.

Option C: The radius of the sphere is half the height of the cylinder.

we know that diameter = 2 × radius (d = 2r)

From option A, we have h = d.

Substitute d = 2r, we get

⇒ h = 2r

Divide by 2 on both sides, we get

$\Rightarrow \frac{h}{2}=r

Therefore, it is true.

Option D: The diameter of the sphere is equal to the radius of the cylinder.

It is not true, because diameters of both cylinder and sphere are equal.

Option E: The volume of the sphere is two-thirds the volume of the cylinder.

Radius of cylinder and sphere = r

Height of cylinder h = 2r (by option C)

Volume of cylinder = Volume of sphere

  $\Rightarrow \pi r^2 h = \frac{4}{3} \pi r^3 (formula)

$\Rightarrow \pi r^2 (2r) = \frac{2\times2}{3} \pi r^3

$\Rightarrow 2 \pi r^3= \frac{2}{3} \times 2\pi r^3

Hence it is true.

Option A, option C and option E are true.

Hatshy [7]3 years ago
6 0

Answer:

Option A,C and E are true

Step-by-step explanation:

Just took quiz on edge nuity 5/19/2020

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Zepler [3.9K]
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Hey there!

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2 years ago
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tekilochka [14]

Given:

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f(x)=\sqrt{7x-21}

To find:

The steps of finding the inverse function f^{-1}(x).

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We have,

f(x)=\sqrt{7x-21}

The steps of finding the inverse function are:

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y=\sqrt{7x-21}

Step 2: Interchange x and y.

x=\sqrt{7y-21}

Step 3: Taking square on both sides, we get

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what are the lengths of the legs of a right triangle in which one acute angle measures 19° and the hypotensue is 15 units long?
givi [52]
Refer to the diagram shown below.

Given:
m∠A = 19°
c = 15

By definition,
sin A = a/c
Therefore
a = c*sin A = 15*sin(19°) = 4.8835

cos A = b/c
Therefore
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Answer:
The lengths are 4.88, 14.18, and 15.00  (nearest hundredth)  

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How many "words" can be written using exactly five A's and no more than three B's (and no other letters)?
kakasveta [241]

This is a problem of Permutations. We have 3 cases depending on the number of B's. Since no more than three B's can be used we can use either one, two or three B's at a time.

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Case 2: Five A's and Two B's

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8 0
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