A solid S is made up of a cylindrical part and conical part. The height of the Soild is 4.5m. The common radius of the cylindrical part and the conical part is 0.9m. The height of the conical part is 1.4m.
a. Calculate the volume,correct to 1 decimal place,of soild S.
I assume you know how to find the volume of a cylinder and a cone.
Clearly, the cylinder's height is 3.1
Now just plug and chug.
To calculate the volume of solid S, we need to find the volumes of the cylindrical part and the conical part separately, and then add them together.
1. Volume of the cylindrical part (Vc):
The formula to calculate the volume of a cylinder is Vc = πr^2h, where r is the radius and h is the height.
Given:
Radius (r) = 0.9m
Height (h) = 4.5m
Substituting the values into the formula:
Vc = π(0.9^2)(4.5)
= π(0.81)(4.5)
≈ 10.24 m³ (rounded to one decimal place)
2. Volume of the conical part (Vco):
The formula to calculate the volume of a cone is Vco = (1/3)πr^2h, where r is the radius and h is the height.
Given:
Radius (r) = 0.9m
Height (h) = 1.4m
Substituting the values into the formula:
Vco = (1/3)π(0.9^2)(1.4)
= (1/3)π(0.81)(1.4)
≈ 0.93 m³ (rounded to one decimal place)
3. Total volume of solid S (Vs):
The total volume of the solid is the sum of the volume of the cylindrical part and the volume of the conical part.
Vs = Vc + Vco
= 10.24 + 0.93
≈ 11.17 m³ (rounded to one decimal place)
Therefore, the volume of solid S is approximately 11.17 m³.