U8L8: Sample work (1pt for correct answer and 1 pt for showing work = 10pts total)
UNITS ARE NEEDED FOR FULL CREDIT
1. Find surface area of right rectangular prism with edge lengths of 8 inches. Proper units.
2. Surface area of bag is 800 sq inches. The overhead bin to put them in is 102x36x33 inches. How many of the bags will fit in the overhead bin?
3. Find surface area of a square pyramid with “a” of .5cm and “l” of .8cm. Round to tenth and proper units.
4. Find volume of right rectangular prism with area of base of 10 in^2 and height of 4 inches. Proper units
5. Find volume of rectangular pyramid with length of 30cm, width of 20 cm and altitude of 40cm. Proper units
1. The surface area of a rectangular prism is given by the formula: 2lw + 2lh + 2wh, where l, w, and h are the lengths of the edges.
Plugging in the given values, we have:
Surface area = 2(8)(8) + 2(8)(8) + 2(8)(8)
Surface area = 128 + 128 + 128
Surface area = 384 square inches
2. To find the volume of the bag, we need to find the volume of the overhead bin and divide it by the surface area of the bag.
Volume of overhead bin = length x width x height
Volume of overhead bin = 102 x 36 x 33
Volume of overhead bin = 112,248 cubic inches
To find how many bags can fit in the overhead bin, we divide the volume of the bin by the surface area of the bag:
Number of bags = (Volume of overhead bin) / (Surface area of bag)
Number of bags = 112,248 / 800
Number of bags ≈ 140.3
Since we can't have a fraction of a bag, we can fit 140 bags in the overhead bin.
3. The surface area of a square pyramid is given by the formula: A = a^2 + 2al, where a is the length of one side of the base and l is the slant height.
Plugging in the given values, we have:
Surface area = (0.5)^2 + 2(0.5)(0.8)
Surface area = 0.25 + 0.8
Surface area = 1.05 square cm
4. The volume of a rectangular prism is given by the formula: Volume = base area x height.
Plugging in the given values, we have:
Volume = 10 in^2 x 4 inches
Volume = 40 cubic inches
5. The volume of a rectangular pyramid is given by the formula: Volume = (length x width x height) / 3.
Plugging in the given values, we have:
Volume = (30 cm x 20 cm x 40 cm) / 3
Volume = 24,000 cubic cm.