A cone with radius 2 units is shown below. Its volume is 29 cubic units. Find the height of the cone. Use 3.14 for \piπpi and round your final answer to the nearest hundredth.

h≈6.93 units

Step-by-step explanation:

To find the height of a cone with radius 2 units and volume of 29 cubic unit, we will follow the steps below;

first, write down the formula for finding the volume of a cone;

v=πr²

where v is the volume of the cone

r is the radius of the cone  and

h is the height of the cone

From the question given, radius r = 2 units   and   volume v = 29 units³

π = 3.14

We can now proceed to insert the values into the formula and then solve for h

v=πr²

29 = 3.14 × 2² ×

29= 3.14 × 4 ×

29= 12.56 ×

29 =

Multiply both-side of the equation by 3

29 × 3 = × 3

At the right-hand side of the equation 3 will cancel-out 3

87 = 12.56 h

Divide both-side of the equation by 12.56

87/12.56 = 12.56 h /12.56

At the right-hand side of the equation 12.56 will cancel-out 12.56 leaving us with just h  while on the left-hand side of the equation 87 will be divided by 12.56

6.926756 = h

h = 6.926756

h≈ 6.93 to the nearest hundredth

h≈6.93 units

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mathpapa

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