A lead pencil is in the shepe of a cylinder. The pencil is 21cm long with radius 0.4 cm and its lead is of radius 0.1 cm.what is the volume of wood in the pencil?
find the volume of the pencil with lead, and then subtract the volume of the lead.
To find the volume of wood in the pencil, we need to subtract the volume of the lead from the total volume of the pencil.
The total volume of the pencil can be calculated using the formula for the volume of a cylinder:
V_total = π × r² × h
Where:
- V_total is the total volume of the cylinder (pencil)
- π (pi) is a constant value approximately equal to 3.14159
- r is the radius of the cylinder (pencil)
- h is the height of the cylinder (pencil)
Given:
- The radius of the pencil (r) is 0.4 cm.
- The height of the pencil (h) is 21 cm.
Substituting the values into the formula, we get:
V_total = 3.14159 × (0.4 cm)² × 21 cm
Now, let's calculate the volume of the lead.
The volume of the lead can also be calculated using the formula for the volume of a cylinder:
V_lead = π × r_lead² × h_lead
Given:
- The radius of the lead (r_lead) is 0.1 cm.
- The height of the lead (h_lead) is the same as the height of the pencil since the lead runs through the entire length.
Substituting the values into the formula, we get:
V_lead = 3.14159 × (0.1 cm)² × 21 cm
Finally, we can find the volume of wood in the pencil by subtracting the volume of the lead from the total volume of the pencil:
V_wood = V_total - V_lead
Now, you can plug in the values and calculate the volume of wood in the pencil.