A can of aerosol deodorant has a cylindrical shape with a hemisphere on top. The diameter of the cylinder is 6cm and the height of the cylinder is 17cm.Calculate the total volume of the can of deodorant?
cap: 2/3 pi r^3
can: pi r^2 h
you have r=3, h=17
plug and chug
(Pi) (3^2) (17)
=480.7
that's the can
add the cap (18pi) for total volume.
To calculate the total volume of the can of deodorant, we need to find the volume of the cylindrical portion and add it to the volume of the hemisphere on top.
1. Volume of the cylindrical portion:
The formula to calculate the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height.
Given:
Diameter of the cylinder = 6 cm
Radius (r) = diameter / 2 = 6 cm / 2 = 3 cm
Height (h) = 17 cm
Now, let's calculate the volume of the cylindrical portion using the formula:
V_cylinder = π(3 cm)² × 17 cm
= π(9 cm²) × 17 cm
= π × 9 cm² × 17 cm
= 153π cm³
2. Volume of the hemisphere:
The formula to calculate the volume of a hemisphere is V = (2/3)πr³, where V is the volume and r is the radius.
Given:
Radius (r) = 3 cm
Now, let's calculate the volume of the hemisphere using the formula:
V_hemisphere = (2/3)π(3 cm)³
= (2/3)π(27 cm³)
= (2/3) × π × 27 cm³
= 18π cm³
3. Total volume:
To find the total volume of the can of deodorant, we add the volume of the cylindrical portion to the volume of the hemisphere.
Total Volume = V_cylinder + V_hemisphere
= 153π cm³ + 18π cm³
= 171π cm³
Therefore, the total volume of the can of deodorant is 171π cm³.