A round pencil is sharpened to a cone shape at both ends as shown in the image below. Use the data in the image and the value 22/7 for π to find the volume of the pencil.
Ugwoke CharlesFebruary 03, 20250
Question: A round pencil is sharpened to a cone shape at both ends as shown in the image below. Use the data in the image and the value 22/7 for π to find the volume of the pencil.
Solution
To find the volume of the pencil, we need to calculate the volume of two parts:
The cylindrical part (the main body of the pencil)
The two conical tips (sharpened ends)
Given dimensions:
Cylinder (main body of pencil)
Radius =
Height = 16 cm
Each cone (sharpened tip)
Radius = cm (same as the cylinder)
Height = cm
There are two cones
Step 1: Volume of the cylindrical part
The volume of a cylinder is given by:
Substituting the values:
Step 2: Volume of the conical tips
The volume of a cone is given by:
Substituting the values for one cone:
Since there are two cones, the total volume of the conical parts is:
Step 3: Total Volume of the Pencil
Thus, the approximate volume of the pencil is 14.45 cm³.