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murzikaleks [220]
3 years ago
15

Find the volume of a cone with a height of 12 yd and a base diameter of 10 yd.

Mathematics
1 answer:
anyanavicka [17]3 years ago
4 0

Answer:

The volume of the cone is 314yd³

Step-by-step explanation:

radius = half of diameter

d = 10yd

r = 10yd / 2 = 5yd

First of all to solve this problem we have to know the formula to calculate the volume of a cone

v = volume

r = radius  = 5yd

h = height  = 12yd

π = 3.14

v = 1/3 * π * r² * h

we replace with the known values

v = 1/3 * 3.14 * (5yd)² * 12yd

v = 1/3 * 3.14 * 25yd² * 12yd

v = 314yd³

The volume of the cone is 314yd³

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lesya692 [45]

There are three possible outcomes that you may encounter when working with these system of equations:


  •    one solution
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We are going to try and find values of x, y, and z that will satisfy all three equations at the same time. The following are the equations:

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We are going to use elimination(or addition) method

Step 1: Choose to eliminate any one of the variables from any pair of equations.

In this case it looks like if we multiply the third equation by 4 and  subtracting it from equation 1, it will be fairly simple to eliminate the x term from the first and third equation.

So multiplying Left Hand Side(L.H.S) and Right Hand Side(R.H.S) of 3rd equation with 4 gives us a new equation 4.:

4. 4x-20y-12z = 20      

Subtracting eq. 4 from Eq. 1:

(L.HS) : 4x-2y+5z-(4x-20y-12z) = 18y+17z

(R.H.S) : 20 - 6 = 14

5. 18y+17z=14

Step 2:  Eliminate the SAME variable chosen in step 2 from any other pair of equations, creating a system of two equations and 2 unknowns.

Similarly if we multiply 3rd equation with 3 and then subtract it from eq. 2 we get:

(L.HS) : 3x+3y+8z-(3x-15y-9z) = 18y+17z

(R.H.S) : 4 - 15 = -11

6. 18y+17z = -11

Step 3:  Solve the remaining system of equations 6 and 5 found in step 2 and 1.

Now if we try to solve equations 5 and 6 for the variables y and z. Subtracting eq 6 from eq. 5 we get:

(L.HS) : 18y+17z-(18y+17z) = 0

(R.HS) : 14-(-11) = 25

0 = 25

which is false, hence no solution exists



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