Question

The cone in Fig. 15.29 is exactly half full of water

Answer 1

Answer:

The water is 8 cm deep.

Step-by-step explanation:

In order to solve this problem we first need to find the total volume of the cone, this is done by using the following formula:

$V = \frac{\pi*r^2*h}{3}\\\\V = \frac{\pi*(6)^2*16}{3}\\\\V = \frac{576*\pi}{3}\\\\V = 192*\pi$

The total volume of the cone is 192*pi cm³, if it is half full then the volume of the water is half of that, which would be 96*pi cm³, we can apply this value to the same formula in order to find the height of the water:

$96\pi = \frac{\pi*(6)^2*h}{3}\\\\\pi*36*h = 288\pi\\h = \frac{288}{36}\\h = 8 \text{ cm}$

The water is 8 cm deep.