Find the total surface area of the 3-dimensional figure below.
Jerome is making props for a school play. Jerome’s theater teacher gave him this sketch below and asked him to make 15 plywood pillars that are regular pentagonal prisms.
Since the audience cannot see the top or bottom of the pillars, Jerome has decided to leave those open. Plywood is purchased in rectangular sheets that are 4 feet by 8 feet, and must be purchased by the full sheet. How many sheets of plywood will Jerome have to buy?
A. 1 sheet
Incorrect. One full sheet would be required for each pillar - The height of one pillar is the same as the height of one full sheet of plywood. The width of each panel is 9 inches and there are 5 panels – a total of 45 inches or 3.75 feet (45 divided by 12 equals 3.75) needed for each pillar. This is the almost the width of one sheet of plywood. There are 15 pillars, so 15 sheets of plywood are necessary.
B. 15 sheets
Correct! You found the amount of area of one sheet will cover 1 pillar, but there are 15 pillars, therefore you needed 15 sheets.
C. 14 sheets
Incorrect. Jerome must purchase full sheets of plywood. One full sheet would be required for each pillar - The height of one pillar is the same as the height of one full sheet of plywood. The width of each panel is 9 inches and there are 5 panels – a total of 45 inches or 3.75 feet (45 divided by 12 equals 3.75) needed for each pillar. This is the almost the width of one sheet of plywood. There are 15 pillars, so 15 sheets of plywood are necessary.
D. 34 sheets
Incorrect. One full sheet would be required for each pillar - The height of one pillar is the same as the height of one full sheet of plywood. The width of each panel is 9 inches and there are 5 panels – a total of 45 inches or 3.75 feet (45 divided by 12 equals 3.75) needed for each pillar. This is the almost the width of one sheet of plywood. There are 15 pillars, so 15 sheets of plywood are necessary.
Betty is remodeling her kitchen and wants her island countertop to look like granite, but granite is too expensive. She has decided to cover the countertop with a plastic laminate that looks like granite.
The countertop is 7 feet long, 2 feet wide and 1 ½ inches thick. There will be a hole 24 inches long and 18 inches wide cut out of the center for the stovetop. The countertop will have laminate on the outside edges and the top. The installer charges by the square foot, excluding cutout areas. How many square feet should Betty plan to pay for?
A. 1908 square feet
Incorrect. You did all the calculations correctly but forgot to change to square feet by dividing your answer by 144, the number of square inches in one square foot.
B. 16.25 square feet
Incorrect. You did all the calculations correctly but forgot to remove the cutout area.
C. 18 square feet
Incorrect. Change the measurements to feet OR inches then find the area of the top, the area of the cutout and subtract it from the area of the top. Now add the area of the four sides to the above answer. If you did your calculations in inches change them to feet by dividing by 144, the number of square inches in one square foot.
D. 13.25 square feet
Correct! You made sure to keep your units correct and made sure to account for taking out the area of the cutout for the stove top.
Salina wants to make a model of the glass rainforest pyramid at Moody Gardens in Galveston. She plans to use clear plastic, instead of glass, to cover the lateral surface area of her pyramid. The base of Salina’s pyramid is going to be 16 inches square. The height of the pyramid will be 15 inches.
How much clear plastic will Salina need to cover the lateral area of her pyramid model?
A. 544 square inches
Correct! In this case, only the lateral sides need to be found.
B. 800 square inches
Incorrect. The question asked for lateral surface area, not total surface area.
C. 1280 square inches
Incorrect. To find the lateral surface area, first find the slant height of the pyramid to use to find the area of one of the triangles, since the base is a square multiply the area by four to obtain the lateral area.
D. 480 square inches
Incorrect. To find the lateral surface area, first find the slant height of the pyramid to use to find the area of one of the triangles, since the base is a square multiply the area by four to obtain the lateral area.
The World Cultures Club at Rio Ranch High School wants to build a scale model of the Great Pyramid of Giza for their upcoming culture fair. The model, including the base, will be built out of wood and the lateral faces will be painted to look like an Egyptian pyramid. After some research, members of the club discovered that the Great Pyramid of Giza was originally 480 feet high at its highest point and measured 756 feet on each side. They figured that their scale model will be about 10 feet high at the top, when completed. The square base will measure 15.75 feet on each side and the slant height of each triangular face will be 12.75 feet.
About how many square feet of wood will the World Cultures Club have to use to build its pyramid model?
A. 1394 sq ft
Incorrect. To find the total surface area find the area of the triangle, 15.75 + 12.75 divided by 2, multiply it by 4 (4 congruent sides) and ADD the area of the base,15.75 × 15.75 to it. 15.75 + 12.75 divided by 2 + 15.75 × 15.75.
B. 650 sq ft
Correct! Good job including the area of the square base into the total surface area.
C. 2008 sq ft
Incorrect. To find the total surface area find the area of the triangle, 15.75 + 12.75 divided by 2, multiply it by 4 (4 congruent sides) and ADD the area of the base,15.75 × 15.75 to it. 15.75 + 12.75 divided by 2 + 15.75 × 15.75.
D. 1051 sq ft
Incorrect. To find the total surface area find the area of the triangle, 15.75 + 12.75 divided by 2, multiply it by 4 (4 congruent sides) and ADD the area of the base,15.75 × 15.75 to it. 15.75 + 12.75 divided by 2 + 15.75 × 15.75.