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 using the formula: 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height.
In this case, the edge length is given as 8 inches. Since it is a right rectangular prism, all the edges are equal.
Therefore, the length (l), width (w), and height (h) are all 8 inches.
Substituting the values into the formula, we get:
Surface area = 2(8)(8) + 2(8)(8) + 2(8)(8) = 128 + 128 + 128 = 384 square inches.
2. The volume of the overhead bin can be found by multiplying the length, width, and height together.
The dimensions of the bin are given as 102x36x33 inches.
Volume = 102 x 36 x 33 = 119,088 cubic inches.
To find out how many bags can fit in the bin, we need to divide the volume of the bin by the surface area of each bag.
The surface area of each bag is given as 800 square inches.
Number of bags = Volume of bin / Surface area of each bag
Number of bags = 119,088 / 800 = 148.86
Since we cannot have a fraction of a bag, the maximum number of bags that can fit in the bin is 148 bags.
3. The surface area of a square pyramid can be found using the formula: A = a^2 + 2a√((l/2)^2 + h^2), where a is the length of the base side, l is the slant height, and h is the height.
In this case, a is given as 0.5 cm and l is given as 0.8 cm.
Substituting the values into the formula, we get:
A = (0.5)^2 + 2(0.5)√((0.8/2)^2 + (0.8)^2) = 0.25 + 2(0.5)√(0.16 + 0.64) = 0.25 + 2(0.5)√(0.8) = 0.25 + 2(0.5)(0.8944) = 0.25 + 0.8944 = 1.1444 square cm (rounded to the nearest tenth).
4. The volume of a rectangular prism can be found by multiplying the area of the base by the height.
In this case, the area of the base is given as 10 in^2 and the height is given as 4 inches.
Volume = 10 in^2 x 4 inches = 40 cubic inches.
5. The volume of a rectangular pyramid can be found by multiplying the length, width, and height together, and then dividing by 3.
In this case, the length is given as 30 cm, the width is given as 20 cm, and the altitude (height) is given as 40 cm.
Volume = (30 cm x 20 cm x 40 cm) / 3 = 24,000 cubic cm.
2,3, and 5 are wrong
Apologies for the mistakes. Here are the correct solutions:
2. The volume of the overhead bin can be found by multiplying the length, width, and height together.
The dimensions of the bin are given as 102x36x33 inches.
Volume = 102 x 36 x 33 = 119,088 cubic inches.
To find out how many bags can fit in the bin, we need to divide the volume of the bin by the volume of each bag.
The surface area of each bag is given as 800 square inches, but we need to find the volume of the bag.
Assuming the bag is a rectangular prism, we do not have enough information to calculate the volume of the bag. Please provide the necessary dimensions or clarify the shape of the bag for an accurate answer.
3. The surface area of a square pyramid can be found using the formula: A = a^2 + 2a√((l/2)^2 + h^2), where a is the length of the base side, l is the slant height, and h is the height.
In this case, a is given as 0.5 cm and l is given as 0.8 cm.
Substituting the values into the formula, we get:
A = (0.5)^2 + 2(0.5)√((0.8/2)^2 + (0.5)^2) = 0.25 + 2(0.5)√(0.16 + 0.25) = 0.25 + 2(0.5)√(0.41) = 0.25 + 2(0.5)(0.641) = 0.25 + 0.641 = 0.891 square cm (rounded to the nearest tenth).
5. The volume of a rectangular pyramid can be found by multiplying the length, width, height, and dividing by 3.
In this case, the length is given as 30 cm, the width is given as 20 cm, and the altitude (height) is given as 40 cm.
Volume = (30 cm x 20 cm x 40 cm) / 3 = 8000 cubic cm (rounded to the nearest cubic cm).