Question

A cone has a volume of 3533.5 cubic inches and a radius of 15 inches. What is its height?

Answer 1

Answer:

• 15 in

Step-by-step explanation:

Volume of the cone:

• V = 1/3πr²h

Given:

• V = 3533.5 in³
• r = 15 in

Find the value of h:

• h = 3V/(πr²)

Substitute the values and calculate:

• h = 3*3533.5/(3.14*15²)
• h = 15 in

Answer 2

Answer:

   h=14.9966

Step-by-step explanation:

1. The formula of the volume is:

        V=$\frac{ab(h)}{3}$

2. So you have to substitute the the data that you have:

       3533.5$in^{3}$=$\frac{ab(h)}{3}$

3. To have the area of the base (ab) you have to get the formula of the circle's area and solve:

       A=$\pi$($r^{2}$)

       A=$\pi$($15^{2}$)

       A=3.1416(225)

       A=706.86in

4. Now you have the area of the base:

        3533.5$in^{3}$=$\frac{706.86(h)}{3}$

5. In this step you are going to clear the variable which is the heigh (h) and solve as an equation:

         3533.5$in^{3}$=$\frac{706.86(h)}{3}$

     3533.5$in^{3}$(3)=706.86(h)

               $\frac{10,600.5}{706.86}$=h

                       h=14.9966

The result may vary depending on the value of $\pi$ that you use,