Rectangles
2L + 2W OR 2(L+W)
What is the simplified expression for the surface area of a square based prism when its surface area is minimized for a given volume?
6s2
What is the simplified expression for the surface area of a cylinder which has the maximum volume for a given surface area?
6(pi)r2
A garden is to be constructed up against the side of a house so that only 3 sides need to be constructed. If there are 24 meters of material available, what will be the dimensions of the garden?
6 × 12 m
Parallel or overlapping.
True or false: For a given area, the perimeter of a rectangle is minimized when the length is twice the width.
False, The perimeter is minimized when the length is equal to the width (square)
What is the simplified expression for the volume of a square based prism when the volume is maximized for a given surface area?
V = s3
What is the simplified expression for the volume of a cylinder when the smallest surface area is used to enclose a given volume.
2(pi)r3
A movie theatre used square based prisms for their popcorn containers. What is the maximum volume that can be enclosed if the base length is 6 cm?
216 cm3
Two lines are perpendicular if their slopes are _______ ______ of each other
Negative reciprocal.
What is the maximum area that can be enclosed by a rectangle with a perimeter of 24 units?
36 square units
What is the maximum surface area that a square based prism can have if it encloses a volume of 1000 cubic units?
600 square units
What is the maximum volume that can be enclosed by a cylinder with a surface area of 1000 square units.
2428 cubic units
What is the volume of the largest gift box that can be wrapped with 54 cm2 of remaining gift wrap?
27 cm3
Would substitution or elimination be easier to solve the following system:
2x - 5y = 8
4y - 2x = 13
Elimination
What is the minimum perimeter of a rectangle that can enclose an area of 16 square units?
16 units
What is the maximum volume that a square based prism can enclose if it has a surface area of 150 square units.
125 cubic units.
What is the minimum surface area of a cylinder which encloses a volume of 1600 cubic units?
757 square units
A cylindrical mug is designed to minimize heat loss. If there is no lid, what is the surface area required to enclose 350 mL of liquid?
661 cm2
Find the solution of:
2x - 4y = 6
8y - 8 = 2x
(10, 7/2)
What is the area of the largest rectangle that can fit in a circle of radius 6 units?
72 units squared
A square based prism is missing two of its faces. What is the minimum surface area of the prism if it encloses an area of 729 cubic units.
324 square units.
A cylinder has only one face. What is the radius if it encloses a volume of 2000 cubic units?
6.8 units
A pipe is constructed out of 320 cm2 of steel. If the volume is maximized to increase water flow, what is the volume enclosed by the pipe?
807 cm3
Find the intersection of the following lines:
y = 2x - 1/2
-8x = -4y+4
No solutions, parallel!