1) A popcorn company makes two different size popcorn tins with the same base dimensions. The small size has a height that is equal to its radius. The medium size has a height that is \(1.5\) times the radius.
a) Find the surface area of each tin in terms of the radius.
b) Which popcorn size is more efficient?
c) What would be your recommendation for the price comparison for each tin be?
a) Find the surface area of each tin in terms of the radius.
b) Which popcorn size is more efficient?
c) What would be your recommendation for the price comparison for each tin be?
2) The management of on ocean life museum will choose to include either Aquarium A or Aquarium B in a new exhibit. They are concerned about cost efficiency.
Aquarium A is a right cylinder with a diameter of \(10\) feet and a height of \(5\) feet. Covering the lower base of Aquarium A is an “underwater mountain” in the shape of a \(5\)-foot-tall right cone. This aquarium would be built into a pillar in the center of the exhibit room.
Aquarium B is half a \(10\)-foot-diameter sphere attached to the ceiling of the exhibit room.
Determine which aquarium is more cost efficient. That is, which aquarium will hold the most water for the least amount of glass material? Justify your answer.
Aquarium A is a right cylinder with a diameter of \(10\) feet and a height of \(5\) feet. Covering the lower base of Aquarium A is an “underwater mountain” in the shape of a \(5\)-foot-tall right cone. This aquarium would be built into a pillar in the center of the exhibit room.
Aquarium B is half a \(10\)-foot-diameter sphere attached to the ceiling of the exhibit room.
Determine which aquarium is more cost efficient. That is, which aquarium will hold the most water for the least amount of glass material? Justify your answer.
3.) Pipes can be stacked in a staggered pattern or non-staggered pattern.
a) How much shorter are \(20\) layers of staggered pipe stacks?
b) How many layers make the staggered pipes more efficient?
a) How much shorter are \(20\) layers of staggered pipe stacks?
b) How many layers make the staggered pipes more efficient?