b. 24 in3
c. 36 in3
d. 48 in3
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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120 + 110 = 1,500d + 2,500d
120d + 1,500 = 110d + 2,500
120d + 2,500 = 110d + 1,500
Answer:
C
Step-by-step explanation:
Job A:
Job B:
Solving these 2 equations for would tell us after how many days both job would pay the same. Answer choice C is correct.