Question

the hourglass shown below is made up of two identical cones. each cone has a height of 6 centimeters and a diameter of 8 centimeters. what is the volume of the hourglass to the nearest cubic centimeter? use the π key to calculate the answer. \boxed{} cm³

Explanation:

Step1: Find the radius of the cone

The diameter of the cone is 8 cm, so the radius \( r=\frac{8}{2} = 4\) cm.

Step2: Recall the volume formula for a cone

The volume of a cone is given by \( V=\frac{1}{3}\pi r^{2}h\), where \( r\) is the radius and \( h\) is the height.

Step3: Calculate the volume of one cone

Substitute \( r = 4\) cm and \( h=6\) cm into the formula: \( V_{1}=\frac{1}{3}\pi\times4^{2}\times6=\frac{1}{3}\pi\times16\times6 = 32\pi\) cubic centimeters.

Step4: Calculate the volume of the hourglass (two cones)

Since the hourglass is made of two identical cones, the total volume \( V = 2\times V_{1}=2\times32\pi=64\pi\).
Using the \(\pi\) key, \( 64\pi\approx64\times3.1415926535 = 201.0619298\approx201\) (to the nearest cubic centimeter).

Answer:

201