Question

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.

Answer 1

Answer:

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$\frac{h}{3}$

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$\frac{h}{3}$

29 = 3.14 × 2² × $\frac{h}{3}$

29= 3.14 × 4 × $\frac{h}{3}$

29= 12.56 × $\frac{h}{3}$

29 =$\frac{12.56h}{3}$

Multiply both-side of the equation by 3

29 × 3 =$\frac{12.56h}{3}$ × 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