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Allisa [31]
3 years ago
12

A sphere has a radius of 15 m. If the radius is divided by 5, what is the effect on the surface area? HELP PLEASE!!

Mathematics
2 answers:
Yakvenalex [24]3 years ago
8 0

i got 3 and the teacher said it was right

eduard3 years ago
8 0

Answer:

The surface area is divided by 25.

Step-by-step explanation:

The radius of a sphere is given as 15 m.

To obtain the surface area of the original sphere, substitute the radius length into the formula for the surface area of a sphere, S=4πr2.

S=4π(15)2=(4)(225)π=900π

The surface area of the original sphere is 900π m2.

To find the radius of the new sphere divide the radius of the original sphere by 5.

r=155=3

The radius of the new sphere is 3 m.

To obtain the surface area of the new sphere, substitute the radius length into the formula for the surface area of a sphere, S=4πr2.

S=4π(3)2=(4)(9)π=36π

The surface area is 36π m2.

Notice that 900π=25(36π). The surface area of the second sphere is 52=25 times less than the original surface area. The surface area of a sphere changes by the square of the factor that the radius changes.

Therefore, the surface area is divided by 25.

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kati45 [8]
78


step by step explanation:

first: divide 600 and 15

answer to 600/15: 40

second: divide 3120 and 40

final answer: 78
5 0
3 years ago
The area of a square is tripled by adding 10 cm to one dimension and 12 cm to the other. Determine the side length of the square
Rina8888 [55]
Area = length *width
A = x²
3x² = (x+10)(x+12)
3x² = x²+10x+12x+120
3x² = x²+22x+120
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0 = -2x²+22x+120
Factor to solve for x: 
-2(x²-11x-60)
(x+4)(x-15)
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4 0
3 years ago
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professor190 [17]

Answer:

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6 0
2 years ago
The fraction of defective integrated circuits produced in a photolithography process is being studied. A random sample of 300 ci
Olenka [21]

Answer:

The correct answer is

(0.0128, 0.0532)

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence interval 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

Z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}

For this problem, we have that:

In a random sample of 300 circuits, 10 are defective. This means that n = 300 and \pi = \frac{10}{300} = 0.033

Calculate a 95% two-sided confidence interval on the fraction of defective circuits produced by this particular tool.

So \alpha = 0.05, z is the value of Z that has a pvalue of 1 - \frac{0.05}{2} = 0.975, so Z = 1.96.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{300}} = 0.033 - 1.96\sqrt{\frac{0.033*0.967}{300}} = 0.0128

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{300}} = 0.033 + 1.96\sqrt{\frac{0.033*0.967}{300}} = 0.0532

The correct answer is

(0.0128, 0.0532)

4 0
2 years ago
What is the measure of angle 1?
Tju [1.3M]
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8 0
3 years ago
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