Post Test: Extending to Three Dimensions
Christi is using a display box shaped like a regular pentagonal prism as a gift box. About how much gift wrap does she need to completely cover the box?
1,020 cm^2
The first attempt of the basic design of a new toy is shown. What is the surface area of the new toy to the nearest square inch?
1,326 in^2
Selim is ordering hollow, concrete spheres to place as barriers in the city park. The spheres cost $2 per square foot, and Selim can spend $20 per sphere. What is the maximum diameter of the spheres he can purchase?
1.78 feet
The diameter of a sphere measures 10.4 inches. What is the surface area of the sphere?
108.16(pie) in^2
The curved sides of large storage tanks at a refinery need to be painted. What is the approximate area of each tank that will be painted?
2,287 ft^2
The runways at an airport are arranged to intersect and are bordered by an orange fencing as shown in the figure. A security guard needs to patrol along the fencing once per shift. What is the estimated distance they walk every shift?
20,000 ft
The curved parts of the figure are arcs centered at points A and C. What is the approximate length of boundary ABCD? Use the value (pie) = 3.14, and round the answer to one decimal place.
23.1
The school puts up fencing around an area in the shape of a hexagon for an outdoor concert. How much fencing does the school use? Round your answer to the nearest whole yard.
36 yards
A company can make a hollow rubber ball for $0.02 per square foot. Each ball costs the company $1. What is the diameter of a ball to the nearest tenth of a foot?
4.0 feet
The composite figure shown has a surface area of 844 square centimeters. What is the height of the rectangular prism?
5 centimeters
A hotel builds an isosceles trapezoidal pool for children. It orders a tarp to cover the pool when not in use. What is the area of the tarp?
To find the height, first find that D is 60 degrees. This means the height of the trapezoid is approximately 4.3 feet. So, the area of the tarp is approximately 53.7 square feet.
Yolanda says she can use a sphere to model the surface area of the boulders on this beach. Explain whether Yolanda is correct.
correct, no flat surface, sphere
The surface area of a sphere is 320 square centimeters. What is the radius of the sphere? Round your answer to 2 decimals places.
5.05 centimeters
For an art project, a cone is covered with paper without any gaps or overlaps. The height of the cone is 28 inches and its diameter is 14 inches. What is the surface area of the covering to the nearest square inch?
789 in ^2
The surface area of a cone is 216(pie) square units. The height of the cone is 5/3 times greater than the radius. What is the length of the radius of the cone to the nearest foot?
9 feet
A designer makes the sketch shown below for a new lamp. What is the approximate area of her sketch?
The lamp shade is a trapezoid. Its area is approximately 30 square inches. The bases of the lamp are two trapezoids. The area of each is approximately 20 square inches. In total, the area is approximately 70 square inches.
The Pyramid of the Sun in Mexico is a square pyramid. The base edge is approximately 220 meters, and the height is approximately 70 meters. What is the approximate surface area of the sides of the pyramid to the nearest thousand square meters?
The lateral surface area is about 57000.
In the figure, the radius of the partial circle with center A is 4 feet.
The perimeter of the figure is 24.50 feet, and the area of the figure is 45.68 square feet.
The surface area of a cylinder is approximately 640.56 square meters. The radius of the cylinder is 5 meters less than the height of the cylinder. To the nearest whole meter, what are the radius and height of the cylinder?
The radius is approximately 6 meters, and the height is approximately 11 meters.
What figure best models the shell, and what is the approximate surface area of the shell?
The shell is best modeled by a cone. The approximate surface area of the shell is 100.6 square inches.