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Margarita [4]
3 years ago
8

12 spheres of the same size are made from melting a solid cylinder of 1 cm diameter and 2 cm height. Find the diameter of each s

phere.
Mathematics
1 answer:
mars1129 [50]3 years ago
5 0

The answer is: The diameter is 4 centimeters.

The explanation  is shown below:

1. The volume of the cylinder is:

Vc=r^{2}h \pi

Where r is the radius (r=\frac{16cm}{2}=8cm) and h is the height (h=2cm).

Then:

Vc=(8cm)^{2}}(2cm)\pi\\Vc=128\pi

2. The total volume of the 12 spheres is:

Vs=12(\frac{4}{3}r^{3}\pi)\\Vs=16r^{3}\pi

3. The volume of the cylinder and the total volume of all the 12 spheres, are equal, therefore:

Vc=Vs\\128\pi=16r^{3}\pi

4. Now, you must solve for the radius:

r=\sqrt[3]{\frac{128\pi}{16\pi}}\\r=2cm

5. The diameter is:

d=2r\\d=2(2cm)\\d=4cm

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Answer:

-3, 7 = x

Step-by-step explanation:

3|x – 2| + 2 = 17

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3|x - 2| = 15

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x - 2 =  -5 \:  \:  \:  \: \:  \:  \:  \:  \:  \:  \:  \:  \:  x - 2 = 5

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x = -3 x = 7

I am joyous to assist you anytime.

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3 years ago
Es<br> Double a number is equal to the number decreased by five. Find the number.<br> 10<br> Submit
ivanzaharov [21]

Answer:

I think the answer is 7.5, because of this equation: 2x-5=10

7 0
3 years ago
a museum employee surveys a random sample of 350 visitors to the museum. Of those visitors, 266 stopped at the gift shop. Based
Naddika [18.5K]

1748 people are expected to stop at the gift shop out of 2300.

Step-by-step explanation:

Given,

Number of random sampled people = 350

Number of people who stopped at shop = 266

Percentage = \frac{People\ stopped}{Total\ people}*100

Percentage = \frac{266}{350}*100=76\%

Therefore,

76% people would stop at the gift stop.

Number of people = 2300

Expected number = 76% of total

Expected number = \frac{76}{100}*2300

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1748 people are expected to stop at the gift shop out of 2300.

4 0
3 years ago
Find the length of the third side. If necessary, write in simplest radical form.
Mazyrski [523]

Answer:

\boxed {\boxed {\sf 8}}

Step-by-step explanation:

This triangle has a small square, which represents a right angle. Therefore, we can use the Pythagorean Theorem.

a^2+b^2=c^2

Where <em>a</em> and <em>b </em> are the legs of the triangle and <em>c</em> is the hypotenuse.

In this triangle, 7 and √15 are the legs, because these sides make up the right angle. The unknown side is the hypotenuse, because it is opposite the right angle. So, we know two values:

a= 7 \\b= \sqrt{15}

Substitute these values into the formula.

(7)^2+(\sqrt{15})^2=c^2

Solve the exponents.

  • (7)²= 7*7=49

49+ (\sqrt{15})^2=c^2

  • (√15)²=√15*√15=15

49+15=c^2

Add.

64=c^2

Since we are solving for c, we must isolate the variable. It is being squared and the inverse of a square is the square root. Take the square root of both sides.

\sqrt{64}=\sqrt{c^2} \\\sqrt{64}= c\\8=c

The third side length is <u>8.</u>

6 0
3 years ago
Read 2 more answers
-4(-2z + 2) = 6z + 8
Savatey [412]
8z-8=6z+8
8x-6z=8+8
2z=16
Z=8
8 0
3 years ago
Read 2 more answers
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