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 π.)
1,055.04 cm3
A cone is placed inside a cylinder as shown. The radius of the cone is half the radius of the cylinder. The height of the cone is equal to the radius of the cylinder. What is the volume of the cone in terms of the radius, r?
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 .)
1055.4
To find the volume of the air space surrounding the cone inside the cylinder, we need to calculate the volume of the cylinder and subtract the volume of the cone.
The volume of a cylinder can be calculated using the formula V = πr^2h, where r is the radius and h is the height.
In this case, the radius of the cylinder is 5 cm and the height is 16 cm. So, the volume of the cylinder is V_cylinder = π(5^2)(16).
The volume of a cone can be calculated using the formula V = (1/3)πr^2h, where r is the radius and h is the height.
In this case, the radius of the cone is 4 cm and the height is 12 cm. So, the volume of the cone is V_cone = (1/3)π(4^2)(12).
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.
So, the volume of the air space is V_air_space = V_cylinder - V_cone.
Now let's calculate the volumes.
V_cylinder = π(5^2)(16) = π(25)(16) = 400π cm^3 (using the approximation of π as 3.14)
V_cone = (1/3)π(4^2)(12) = (1/3)π(16)(12) = 64π cm^3
V_air_space = V_cylinder - V_cone
V_air_space = 400π - 64π = 336π cm^3
Therefore, the volume of the air space surrounding the cone inside the cylinder is 336π cm^3.
volumespace=volume cylinder-volumecone
= PI*5^2*16 - 1/3 PI 4^2 * 12