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 right rectangular prism can be found by adding up the areas of all six faces. Each face is a rectangle, so the formula for the surface area is 2(length x width + length x height + width x height).
In this case, the length, width, and height are all 8 inches.
Surface area = 2(8 x 8 + 8 x 8 + 8 x 8) = 2(64 + 64 + 64) = 2(192) = 384 square inches.
Therefore, the surface area of the right rectangular prism is 384 square inches.
2. To find out how many bags will fit in the overhead bin, we need to calculate the volume of the bin and the volume of the bag, and then divide the volume of the bin by the volume of the bag.
The volume of the overhead bin is calculated by multiplying the length, width, and height:
Volume of the overhead bin = 102 x 36 x 33 = 112,248 cubic inches.
To find the volume of one bag, we divide the surface area of the bag by the height of the bag:
Volume of one bag = Surface area of bag / height of bag = 800 / 33 = 24.242 cubic inches.
Now, we divide the volume of the overhead bin by the volume of one bag:
Number of bags = Volume of overhead bin / Volume of one bag = 112,248 / 24.242 = 4,621.216 bags.
Since we can't have a fraction of a bag, the maximum number of bags that will fit in the overhead bin is 4,621 bags.
3. The surface area of a square pyramid can be found by adding up the area of the base and the area of the four triangular faces.
The formula for the surface area of a square pyramid is (a^2 + 2al), where "a" is the length of one side of the base and "l" is the slant height.
In this case, a = 0.5 cm and l = 0.8 cm.
Surface area = (0.5^2 + 2 x 0.5 x 0.8) = (0.25 + 0.8) = 1.05 square cm.
Therefore, the surface area of the square pyramid is 1.05 square cm.
4. The volume of a right rectangular prism can be found by multiplying the area of the base by the height.
In this case, the area of the base is 10 in^2 and the height is 4 inches.
Volume = 10 in^2 x 4 inches = 40 cubic inches.
Therefore, the volume of the right rectangular prism is 40 cubic inches.
5. The volume of a rectangular pyramid can be found by multiplying the length, width, and height and then dividing by 3.
In this case, the length is 30 cm, the width is 20 cm, and the altitude (height) is 40 cm.
Volume = 30 cm x 20 cm x 40 cm / 3 = 24,000 cubic cm / 3 = 8,000 cubic cm.
Therefore, the volume of the rectangular pyramid is 8,000 cubic cm.