A cone has a volume of 12 cubic inches. What is the volume of a cylinder that the cone fits exactly inside of? a. 6 in3
b. 24 in3
c. 36 in3
d. 48 in3
Answers
To find the volume of a cylinder that the cone fits exactly inside, we can use the formula for the volume of a cone. By solving for the radius and height of the cone, we can then substitute those values into the formula for the volume of a cylinder to obtain the volume.The correct option is C.
To find the volume of a cylinder that the cone fits exactly inside, we need to understand the relationship between the cone and the cylinder. The volume of a cone can be found using the formula V = (1/3) * π * r^2 * h, where r is the radius and h is the height of the cone. The volume of the cylinder is equal to the volume of the cone, so the volume of the cylinder can also be calculated using the formula V = π * r^2 * h. In this case, the volume of the cone is given as 12 cubic inches. We can set up an equation to find the radius and height of the cone using this volume, and then use those values to find the volume of the cylinder.
Let's solve for the radius and height of the cone:
1.Start with the formula for the volume of a cone: V = (1/3) * π * r^2 * h
2.Substitute the given volume of the cone as 12 cubic inches: 12 = (1/3) * π * r^2 * h
3.Cancel out the 1/3 by multiplying both sides of the equation by 3: 36 = π * r^2 * h
4.Divide both sides of the equation by π to isolate r^2 * h: r^2 * h = 36/π
5.Since we don't have enough information to solve for both r and h, we will express the height h in terms of the radius r.
6.Substitute r^2 * h with 36/π: r^2 * (36/π) = 36/π
7.Simplify the equation by canceling out the π: r^2 * (36/π) = 36/π
8.Multiply both sides of the equation by π/36: r^2 = 1/π
9.Take the square root of both sides to find the radius r: r = 1/√π
10.Now that we have the radius, we can find the height using the equation r^2 * h = 36/π: (1/√π)^2 * h = 36/π
11.Simplify the equation: h = 36
So, the radius of the cone is 1/√π and the height is 36. Using these values, we can calculate the volume of the cylinder:
1. Start with the formula for the volume of a cylinder: V = π * r^2 * h
2. Substitute the values we found for the cone into the formula: V = π * (1/ √π)^2 * 36
3. Simplify the equation: V = 36 cubic inches
the volume of the cylinder that the cone fits exactly inside is 36 cubic inches.
Therefor the correct option is C.
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Volume of a cylinder = r² π h = 3 · V ( cone ) = 3 · 12 = 36 in³
Answer: C )
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It's basically everything that is added to get that number. You do not need a 100's place because a 0 is holding that spot.
Write an equation to represent the possible numbers of cats and dogs that could have been at the
shelter on Wednesday.
Pat said that there might have been 8 cats and 14 dogs at the shelter on Wednesday. Are Pat’s
numbers possible? Use your equation to justify your answer.
Later, Pat found a record showing that there were a total of 22 cats and dogs at the shelter on
Wednesday. How many cats were at the shelter on Wednesday?
Answers
89.50=2.35c+5.50d
If theres 22 dogs and cats in total you can plug in number less than 22 for c(# of cats) and d(# of dogs).
So we try pats numbers 8 cats and 14 dogs so
89.50=2.35(8)+5.50(14)
89.50=18.8+77
89.50=95.8
So pats numbers were wrong so we try different numbers
So i started pluging in numbers from under 22 so i got c is 10 and d is 12 lets try it with the equation
89.50=2.35(10)+5.50(12)
89.50=23.5+66
89.50=89.50 so it works the answer to how many number of dogs and cats is 12 dogs and 10 cats
Final answer:
The equation representing the costs to care for the animals is 2.35c + 5.5d = $89.50. Pat's proposal of 8 cats and 14 dogs does not match the costs. Upon using additional information of the total number of animals being 22, we can solve the system of equations to find that there were 16 cats and 6 dogs at the shelter on Wednesday.
Explanation:
Let's denote the number of cats as c and the number of dogs as d. We know from the cost of care per day per animal that 2.35c + 5.5d = $89.50. This is the equation representing the possible number of cats and dogs at the shelter in terms of costs. For Pat's numbers, we can substitute c=8 and d=14 into the equation and check if they are possible. That is, substitute and check if 2.35(8) + 5.5(14) equals to 89.5. In this case, it does not since the total here comes to more than $89.50. So, Pat's numbers were not possible.
Regarding the total number of animals, we know that c + d = 22. With this equation, we can solve the system of equations to find out the actual number of cats and dogs at the shelter on Wednesday. Solving these two equations, we will find that 16 cats and 6 dogs were present at the shelter on Wednesday.
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4x-14xy
Answers
2x(2-7y)
Answers
Answer:
1
3
4
7
Step-by-step explanation:
this is what i think it might not be right but i tried my best ;3
can i please have brainly
Answer:
1, 4, 6 those are correct
Step-by-step explanation:
Answers
Answers
Answer:
The ratio of beaks to wings in a flock of birds is 1:2.
Step-by-step explanation:
Consider the provided information.
Beaks are the hand and pointed structure that sticks out from a bird's face.
The number of beaks of a bird is one and the number of wings is two.
We need to find the ratio of beaks to wings in a flock of birds
Thus the ratio of beaks to wings in a flock of birds is 1:2.
This shows that there's one beak for each pair of wings.