1. The main show tank has a radius of 70 feet and forms a quarter sphere where the bottom of the pool is spherical and the top of the pool is flat. (Imagine cutting a sphere in half vertically and then cutting it in half horizontally.) What is the volume of the quarter-sphere shaped tank? Round your answer to the nearest whole number. You must explain your answer using words, and you must show all work and calculations to receive credit.2. The holding tanks are congruent. Each is in the shape of a cylinder that has been cut in half vertically. The bottom of each tank is a curved surface and the top of the pool is a flat surface. What is the volume of both tanks if the radius of tank #1 is 35 feet and the height of tank #2 is 120 feet? You must explain your answer using words, and you must show all work and calculations to receive credit.
3. The company is building a scale model of the theater’s main show tank for an investor's presentation. Each dimension will be made one sixth of the original dimension to accommodate the mock-up in the presentation room. What is the volume of the smaller mock-up tank?
Using the information from #3, answer the following question by filling in the blank: The volume of the original main show tank is ____% of the mock-up of the tank.
Answers
Answer:
1. Volume = 5128.67 ft³
The volume if sphere is given by:
V = (4/3)πr³
If the tank is cut into half vertically, then the volume of sphere becomes.
V = (4/3)πr³ / 2
If the tank is cut into half again horizontally, then the volume of the sphere becomes.
V = (4/3)πr³ / 4
Hence, as the main tank forms a quarter sphere, its Volume is given by:
V = (4/3)πr³ / 4
It is given in the question that the radius is 70 ft.
Substitute that in the given formula:
V = (4/3)π(70)³ / 4
V = 5128.67 ft³
2. Volume of tank = 461,814 ft³
Step-by-step explanation:
Congruent tanks implies that both tanks are of identifical shape, form & dimensions. Congruent means that the tanks have the same radius as well as height. Hence, the heights and radii of tanks #1 and #2 are equal and the same.
Let's list out the information given us:
radius(tank #1) = 35 ft ⇒ radius(tank #2) = 35 ft, height(tank #2) = 120 ft ⇒ height(tank #2) = 120 ft
Volume of cylinder = πr²h
The tanks have been cut into half, as such:
Volume of tank = ½πr²h
Volume of tank = Volume(tank #1) + Volume(tank #2)
Since the tanks are congruent (same dimensions), we have:
⇒ ½πr²h + ½πr²h ⇒ πr²h
Volume of tank = π * 35² * 120 = 147,000 π
Volume of tank = 461,814 ft³
3. 1047.2 ft³
Step-by-step explanation:
The following information is missing:
The main show tank has a radius of 60 feet and forms a quarter sphere where the bottom of the pool is spherical and the top of the pool is flat. (Imagine cutting a sphere in half vertically and then cutting it in half horizontally)
The only dimension needed for the main show tank is its radius. Then the model radius will be 1/6 * 60 = 10 feet
The volume of a sphere is:
V = 4/3 * π * r³
For a quarter sphere it is:
V = 4/3 * π * r³ * 1/4
V = 1/3 * π * r³
For the smaller mock-up tank:
V = 1/3 * π * 10³
V = 1047.2 ft³
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Instructions: Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).Consider the functions f(x)=x^2+9x and g(x)=1/x.f(g(-1)) is g(f(1/2)) is
Answers
Answer: 88
Step-by-step explanation:
1. Add 3 and 8 together
3 + 8 = 11
2. Divide 121 by 11
121/ 11 = 11
3. Multiply the amount of paperbacks in the stack of 11 books (8) by 11
11 x 8 = 88
88 Is your answer.
Answers
Answer: 2(z - 12) = 63
Step-by-step explanation:
Our task is to write the following:
- twice the difference of z and 12 equals 63
So first, the difference of z and 12 means we're subtracting z and 12, and it's written this way:
Next, twice that difference is: . The reason why we need to put parentheses is because that way, 2 is multiplied by both z and -12.
This equals 63:
Answer:
2(z - 12) = 63
Step-by-step explanation:
Twice --> 2*
Difference of z and 12 --> (z-12)
Equals 63 --> = 63
If you combine...
2*(z-12) = 63
You can remove the * sign, because there is a bracket next.
2(z - 12) = 63
If this helped, please consider picking this answer as the Brainliest Answer. Thank you!
Answers
Answer:
2.5gramsofCopper
Step-by-step explanation:
• Total ratio = 8 + 2 = 10
Let the grams of copper be y
Grams of copper = 2.5 g
Answers
Answer:
1. B (firefighter question) 2. A (dance lesson fee question) 3. A (dolphin question)
Step-by-step explanation:
1. The firefighters gear PLUS his weight is how much he weighs in total.
2. An added fee is usually represented as a registration fee or staring fee. There was 45w which should represent the fee she paid every week.
3. The dolphin swims at a rate of 25 kilometres per hour. The graph represents the distance the dolphin traveled because in two hours the dolphin would travel 50 kilometres (25 kilometres*2 hours) and so on.
Answer:
B
Step-by-step explanation:
Answers
Step-by-step explanation:
x + y = 16 (*)
x^2 + y^2 = 146 (**)
(*) <=> x= 16-y
substitute x = 16 - y
(**) <=> (16-y)^2 + y^2 = 146
<=> y^2 - 2.16.y + 16^2 + y^2 = 146
<=> 2y^2 - 32y + 110 = 0
<=> y^2 - 16y + 55 = 0
<=> (y-11)(y-5) = 0
<=> y=11 or y= 5
For y = 11, we have x= 16-11=5
For y=5, we have x= 16-5=11
Answer: (x,y) = (11,5) ; (5,11)
Answers
Final answer:
To solve the equation c = a(w/150) for 'w', divide the equation by 'a' and then multiply by 150. This gives us w = 150c/a. This equation represents 'w' in terms of 'c' and 'a'.
Explanation:
To solve the equation c = a(w/150) for the variable w, you need to isolate w on one side of the equation. The goal is to express w in terms of c and a.
- First, divide both sides of equation by a. This gives you c/a = w/150.
- Then, multiply both sides by 150 to solve for w. This results in w = 150c/a.
So, the equation solved for w is w = 150c/a.
Learn more about Solving for a Variable here:
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