1) Use the “Efficiency Ratio” to determine which is more efficient.
a) Rectangular Prism 1: \(8.2\) mm x \(9.6\) mm x \(10.1\) mm OR Rectangular Prism 2: \(6.8\) mm x \(8.2\) mm x \(8.7\) mm.
b) Regular Square Pyramid 1: base edge \(3.4\) cm with height \(2.3\) cm OR Regular Square Pyramid 2: base edge
\(5.6\) cm with height \(3.6\) cm.
c) Right Cylinder 1: radius \(13.1\) inches with height \(10.7\) inches OR Right Cylinder 2: radius \(15.9\) inches with
height \(12.5\) inches.
d) Right Cone 1: circumference of base edge \(2\) ft \(3\) inches with height \(11\) inches OR Right Cone 2:
circumference of base edge \(4\) ft \(1\) inch with height \(2\) ft \(1\)inch.
2) Find the value of \(k\) so that the two rectangular prisms have the same Efficiency Ratio.
3) A consumer is comparing two front-loading washing machines to determine which one to purchase.
a) Rectangular Prism 1: \(8.2\) mm x \(9.6\) mm x \(10.1\) mm OR Rectangular Prism 2: \(6.8\) mm x \(8.2\) mm x \(8.7\) mm.
b) Regular Square Pyramid 1: base edge \(3.4\) cm with height \(2.3\) cm OR Regular Square Pyramid 2: base edge
\(5.6\) cm with height \(3.6\) cm.
c) Right Cylinder 1: radius \(13.1\) inches with height \(10.7\) inches OR Right Cylinder 2: radius \(15.9\) inches with
height \(12.5\) inches.
d) Right Cone 1: circumference of base edge \(2\) ft \(3\) inches with height \(11\) inches OR Right Cone 2:
circumference of base edge \(4\) ft \(1\) inch with height \(2\) ft \(1\)inch.
2) Find the value of \(k\) so that the two rectangular prisms have the same Efficiency Ratio.
- Prism 1: \(3\) x \(4\) x \(5\) feet
- Prism 2: \(6\) x \(8\) x \(k\) feet
3) A consumer is comparing two front-loading washing machines to determine which one to purchase.
Machine \(1\):
|
Machine \(2\):
|
Based on the data between these two machines:
a)Which machine has the better efficiency ratio?
b)Which has the better Energy Ratio vs. Volume?
c)Which machine has a better Energy Ratio vs. the amount that can be washed?
4) The earth is close to a sphere and has a mean radius length of \(3959\) miles. The moon is also close to a sphere and has a mean radius length of \(1079\) miles. Use the efficiency ratio to determine which planet is more “efficient.” Explain your answer.
5) An engineer has designed five solids to be as efficient as possible (that is, each shape holds a much volume possible for its surface area). But, the engineer doesn’t know which shape is the most efficient compared to other shapes. Use the dimensions given to calculate the surface area and volume of each shape. Then use the Efficiency ratio to determine what shape is the most efficient. (s is the base edge length for the square pyramid)
a)Which machine has the better efficiency ratio?
b)Which has the better Energy Ratio vs. Volume?
c)Which machine has a better Energy Ratio vs. the amount that can be washed?
4) The earth is close to a sphere and has a mean radius length of \(3959\) miles. The moon is also close to a sphere and has a mean radius length of \(1079\) miles. Use the efficiency ratio to determine which planet is more “efficient.” Explain your answer.
5) An engineer has designed five solids to be as efficient as possible (that is, each shape holds a much volume possible for its surface area). But, the engineer doesn’t know which shape is the most efficient compared to other shapes. Use the dimensions given to calculate the surface area and volume of each shape. Then use the Efficiency ratio to determine what shape is the most efficient. (s is the base edge length for the square pyramid)
6) Two \(8.5\) x \(11\) inch pieces of paper is folded to make cylinders. One is folded landscape and the other is folded portrait. Both then have bases added to them. Use the Efficiency Ratio to determine which cylinder is more efficient.
7) Cone \(1\) has a base circumference of \(200\) mm and a height of \(600\) mm. Cone \(2\) also has a base circumference of \(200\) mm but has a height of \(300\) mm. Predict which cone is more efficient. Explain your reasoning.
8) Grapes, apples and oranges are not spherical, but they model a sphere. Use the formulas spheres to determine which fruit is the most efficient.
9) You parents are thinking of purchasing a new pool for your backyard! They show you two options and asks you to choose. Option \(1\) is a hemisphere with a radius of \(12\) feet. Option \(2\) is an irregular prism with the dimensions shown in the diagram. Impress your parents by calculating which pool would be more efficient. Demonstrate your work mathematically.
8) Grapes, apples and oranges are not spherical, but they model a sphere. Use the formulas spheres to determine which fruit is the most efficient.
- One grape of \(1\) cm in diameter produces \(3.8\) cm\(^3\) of grape juice.
- One apple of \(9\) cm in diameter produces \(2400\) cm\(^3\) of apple juice.
- One orange of \(11\) cm in diameter produces \(4900\) cm\(^3\) of orange juice.
9) You parents are thinking of purchasing a new pool for your backyard! They show you two options and asks you to choose. Option \(1\) is a hemisphere with a radius of \(12\) feet. Option \(2\) is an irregular prism with the dimensions shown in the diagram. Impress your parents by calculating which pool would be more efficient. Demonstrate your work mathematically.