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| 1 | |
Fernando is making a blanket for his llama. He has wool cloth with an area of 2 m2. He plans to hem the edges, and would like the perimeter to be a minimum. What dimensions should he use for the blanket? |
| | A) | 0.5 m by 4.0 m |
| | B) | 1.0 m by 2.0 m |
| | C) | 1.2 m by 1.7 m |
| | D) | 1.4 m by 1.4 m |
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| 2 | |
A box of candies has a square base and is designed for a minimum surface area. if the box holds 64 cm3 of candies, what are the dimensions of the box? |
| | A) | 1 cm by 1 cm by 64 cm |
| | B) | 2 cm by 2 cm by 16 cm |
| | C) | 4 cm by 4 cm by 4 cm |
| | D) | 8 cm by 8 cm by 1 cm |
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| 3 | |
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Lydia used a spreadsheet to design several cylinders with the same volume, but different dimensions, as shown. Which has the smallest surface area? |
| | A) | A |
| | B) | B |
| | C) | C |
| | D) | D |
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| 4 | |
Farmer Macdonald built a storage bin in the shape of a square-based prism using 150 m2 of lumber. Find the maximum volume of corn that the bin could hold. |
| | A) | 25 m3 |
| | B) | 75 m3 |
| | C) | 100 m3 |
| | D) | 125 m3 |
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| 5 | |
Emile bought a length of framing 240 cm long at a garage sale. He plans to make a picture frame with the maximum possible area. What is the maximum area that he can frame? |
| | A) | 240 cm2 |
| | B) | 480 cm2 |
| | C) | 3600 cm2 |
| | D) | 7200 cm2 |
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| 6 | |
The Jumbo package of cornflakes is a square-based prism, and holds 8 L of cornflakes. If the package has been designed to minimize surface area, find the dimensions of the package. |
| | A) | 20 cm by 20 cm by 20 cm |
| | B) | 10 cm by 10 cm by 80 cm |
| | C) | 2 m by 2 m by 2 m |
| | D) | 1 m by 1 m by 8 m |
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| 7 | |
Ranee has 10 000 cm2 of plywood. She can make one large box with a square base, or two identical smaller boxes with the square bases. How does the volume of the one large box compare with the total volume of the two smaller boxes? |
| | A) | The volumes of the same. |
| | B) | The ratio is about 3:2. |
| | C) | The ratio is about 2:3. |
| | D) | The ratio is about 2:1 |
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| 8 | |
A water tank has a cylindrical shape, and has been designed to minimize surface area. If the tank holds 120 m3 of water, find the radius. |
| | A) | 5.4 m |
| | B) | 5.0 m |
| | C) | 2.7 m |
| | D) | 2.5 m |
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| 9 | |
What is the surface area of the tank in question#9? |
| | A) | 117.8 m2 |
| | B) | 137.4 m2 |
| | C) | 471.2 m2 |
| | D) | 549.7 m2 |
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| 10 | |
A cylinder and a cube have the same surface area of 720 cm2. Both have been optimized for the maximum volume possible. How do the volumes compare? |
| | A) | The volumes are the same. |
| | B) | The cylinder has a larger volume by 168.8 cm3. |
| | C) | The cube has a larger volume by 168.8 cm3. |
| | D) | The volumes are not related. |
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