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Nostrana [21]
2 years ago
10

Can you please help me...Thank you!

Mathematics
1 answer:
ZanzabumX [31]2 years ago
8 0

Answer:

the answer is the last one.

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Consider this sphere inside the cylinder. Which statements are true? Check all that apply. NEED HELP ASAP​
-Dominant- [34]

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.

6 0
3 years ago
Read 2 more answers
What is 17.8 rounded to the nearest tenth
inysia [295]
It would still be 17.8, unless there are more numbers after the 8.
4 0
3 years ago
The Powerball lottery is open to participants across several states. When entering the powerball lottery, a participant selects
mr Goodwill [35]

Answer and Step-by-step explanation:

Number of ways = 59C5 × 35= 59!/(54!*5!)* 35= 175223510

Odds are thus 1 in 175223510

b) 1 million - Number of ways = 59!/(54!*5!) =5006386*35/34 = 5153632

Odds are thus 1 in 5153632

6 0
3 years ago
At 9:00 pm bob leaves his home and starts walking to the bus stop at a constant speed of 9.3 feet per second. bob's house is 432
klio [65]
a. define variables for the quantities that are changing (be specific).
 We define variables:
 t = time in second
 d = distance traveled
 The variables that are changing are t and d.
 As the time increases, the distance decreases.

 b. what does it mean to say bob walks at a constant speed of 9.3 feet per second?
 It means that for every second that passes, Bob walks 9.3 feet.

 c. consider the formula d = 4320 - 9.3t i. what does t represent? ii. what does 9.3t represent? iii. what does d represent? 
 For this case we have:
 t = represents the time in seconds
 9.3t = represents the distance traveled by Bob
 d = represents the distance Bob must travel to get to the bus stop.
5 0
2 years ago
Given that the prime factorisation of 198 is 2x(3×3)x11. State the minimum integer value of
mylen [45]

Answer:

22

Step-by-step explanation:

198 = 2×3²×11

For 198n to be a perfect square, each prime factor must have an even exponent.  So the smallest 198n would be:

198n = 2²×3²×11²

198n = 4356

n = 22

7 0
3 years ago
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