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Artemon [7]
3 years ago
12

The Reunion Tower is one of the most recognizable landmarks in Dallas, Texas due to the giant sphere that sits atop the structur

e. The sphere, which houses observation decks accessible to visitors, has a diameter of 118 feet. Which value is closest to the volume of the dome? Use 3.14 for π.
A. 859,852ft^3
B. 1,679,406ft^3
C. 2,350,879ft^3
D. 2,510,782ft^3
Mathematics
1 answer:
ValentinkaMS [17]3 years ago
6 0
The volume of a sphere uses the following formula:

V = \frac{4}{3}\pi r^{3}

Because the question asks to use 3.14 in place of pi, the formula will now look like this:

V = (\frac{4}{3})(3.14)r^{3} = 4.18\overline{66} r^{3}

We are given a diameter of 118 feet. The radius is half of the diameter, so divide the diameter by 2 to find the radius:

118 \div 2 = 59
r = 59

Plug this value into the formula, and solve with a calculator:

4.18\overline{66} \times 59^3 = 4.18\overline{66} \times 205379 = 859853.413

Although our result is one cubic foot off, the answer is <span>A. 859,852ft^3.

(859,852 is the result if the constant in the given formula is 4.18666, but the result with infinitely repeating numbers is 859,853.)</span>
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0.12x - 1.5= 0.24x - 0.06
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3 years ago
GUYS I NEED HELP PLSSSSSS! Ive been working on this ALL day!
Vika [28.1K]

First, let's write what we know.

We can represent the number of students in the play from each class as L, G, and C. We know that L = 7, and if Gardener has 4 more students than Cho, then G = C + 4.

Then, taking the third line, we can write an inequality:

C < L < G

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3 < C < 7

If C is greater than 3 and less than 7 and is an integer, than means C is 4, 5, or 6.

Then, we need to find how many students are in the play.

C + L + G

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So we have our expression for the number of students in the play. Then, we need to find the total number of students. We know that 2C + 11 will be 30% of the total, so if T is the total, we can find T.

0.3T = 2C + 11

(Divide by 3/10 or multiply by 10/3 on both sides)

T = 20/3 C + 110/3

We know from before that C is 4, 5 or 6. We can plug these into our equation here to find which one produces a whole number.

T = 20/3 * 4 + 110/3

T = 190/3

T = 20/3 * 5 + 110/3

T = 210/3

T = 70

T = 20/3 * 6 + 110/3

T = 230/3

We can see here that only when C is 5 will the total be a whole number. That means Mrs. Cho has 5 students in the play. If Mrs. Gardner has 4 more than that, she has 9 students in the play in her class.  We now need to figure out the number of student in her class.

The total students are Cho's, Logan's, and Gardner's classes added together. We know that Logan's class is 23 students, so if we subtract that from the total, we can see that Cho's and Gardner's class have 47 students. If Mrs. Cho has 24 students in her class, we can subtract that from the 47, so we know that Mrs. Gardner has 23 students in her class.

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Answer:

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