To calculate the amount of glass used for the sculpture, we need to determine the volume of each individual glass component and then multiply it by the total number of components (11,000).
1. Volume of cylindrical stem:
The volume of a cylinder can be calculated using the formula: V = πr^2h, where r is the radius and h is the height.
Given:
Height (h) of cylindrical stem = 40 in
Diameter (d) of cylindrical stem = 1/8 in (radius = d/2 = 1/16 in)
Volume of each cylindrical stem = π(1/16)^2 × 40 = π/256 × 40
2. Volume of cone (head of wheat):
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.
Given:
Height (h) of cone (head of wheat) = 4 in
Base diameter (d) of cone (head of wheat) = 3/4 in (radius = d/2 = 3/8 in)
Volume of each cone (head of wheat) = (1/3)π(3/8)^2 × 4 = (1/3)π/16 × 4
3. Total volume of glass used:
To calculate the total volume of glass, we need to sum up the volumes of all the individual components.
Total volume of glass = (Number of cylindrical stems × Volume of each cylindrical stem) + (Number of cones × Volume of each cone)
= (11,000 × (π/256 × 40)) + (11,000 × ((1/3)π/16 × 4))
Finally, you can simplify and evaluate this expression to find the approximate amount of glass used for the sculpture.