A cylinder has a height of 16 cm and a radius of 5 cm. A cone has a height of 12 cm and a radius of 4 cm. If the cone is placed inside the cylinder as shown, what is the volume of the air space surrounding the cone inside the cylinder? (Use 3.14 as an approximation of ð.)
To find the volume of the air space surrounding the cone inside the cylinder, we need to subtract the volume of the cone from the volume of the cylinder.
First, let's find the volume of the cone. The formula for the volume of a cone is Vc = (1/3)πr^2h, where r is the radius and h is the height. Plugging in the values, we have:
Vc = (1/3) * 3.14 * 4^2 * 12
= (1/3) * 3.14 * 16 * 12
= (1/3) * 3.14 * 192
= 201.792 cm^3 (approx.)
Now, let's find the volume of the cylinder. The formula for the volume of a cylinder is Vcy = πr^2h, where r is the radius and h is the height. Plugging in the values, we have:
Vcy = 3.14 * 5^2 * 16
= 3.14 * 25 * 16
= 1256 cm^3 (approx.)
Finally, to find the volume of the air space surrounding the cone inside the cylinder, we subtract the volume of the cone from the volume of the cylinder:
Volume of air space = Vcy - Vc
= 1256 - 201.792
= 1054.208 cm^3 (approx.)
Therefore, the volume of the air space surrounding the cone inside the cylinder is approximately 1054.208 cm^3.