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Section 8.1 : Determining the Optimum Area and Perimeter

1. Determine the maximum area of a rectangle with a perimeter of

a) 232 km b) 56 m c) 192km

2. Determine the minimum perimeter for a rectangle with each area. Round your answer to the nearest 10th

ofa unit.

a) 242 cm2 b) 1240 m2 c) 60 000 cm2

3. Make a chart of the possible dimensions for a rectangle with an area of 196 m2. What are the optimumdimensions of the rectangle for minimizing the perimeter?

Make a chart of the possible dimensions for a rectangle with a perimeter of 44 m. What are the optimum

dimensions for maximizing the area of the rectangle?

4. Each of the following rectangles ahs a border on three sides. The area of each rectangle is given. Determine

the optimum length of their sides in order to minimize boarder length.

a) 72 km2 b) 162 m2 c) 512 cm2

Section 8.2 : Problems Involving Composite Shapes

1. Calculate the shaded area of the figures below. Round your answer to the nearest 10 th of a unit.

2. Calculate the area and the perimeter of each of the following shapes. Round your answers to one decimalplace.

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Section 8.3: The Pythagorean Theorem

1. Determine the missing length. Round your answers to one decimal place

2. Determine the length of each missing side of the triangle. Round your answer to one decimal place.

Section 8.4: Surface Area of Right Pyramids and Cones

1. Find the surface area of the following right pyramids. Round your answers to one decimal place

2. Find the surface area of the following cones

3. Find the surface area of a cone with a height of 4.0 km and a base area of 28.3 km2

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Section 8.5: Volumes of Pyramids and Cones

1. Calculate the volume of the following regular pyramids

2. Calculate the volume of the following cones

3. Find the height of a cone that has a radius of 2 cm and a volume of 23 cm3.

4. A cylinder has a volume of 2120.6cm3 and a base radius of 5 cm. What is the volume of a cone with thesame height but a base radius of 2.5 cm?

Section 8.6: Volume and Surface Area of a Sphere

1. Determine the surface are and volume of the following shapes

2. Find the surface area and volume of the following shapes

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3. Eight basketballs are put into a holding container. The radius of each basketball is 10cm. How much roomwill be left in the container if the container is shaped like a square based pyramid with each side of the base

measuring 40 cm and with a height of 70 cm?

Section 8.8: Optimum Volume and Surface Area

1. Determine the least possible surface area of each object if it is a square based prism. Now determine theleast possible surface area for each object if it is a sphere. Which area is smaller? Round yourfinal answer

to one decimal place.

a) 6859 m3 b) 6028.6cm3

2. Determine the least possible surface area for a cylinder with the following volumes. Round your answers to

one decimal place.

a) 3217.0m3 b) 169.6mm3

3. Two shapes both have a surface are of 1200cm2. One of them is a cylinder and one of them is a squarebased prism.

a) What is the maximum value of the volume of the shape if it is a cylinder?

b) What is the maximum value of the volume of the shape if it is a square based prism?

c) Which shape should you chose for a container you are building if you want the greatest possiblevolume and the least possible surface are?