Find the capacity of a rectangular cistern in litres whose dimensions ...
Cisterns are cuboidal in shape.
dimension = 11.2m x 6m x5.8m
capacity = volume = lbh = 11.2m x 6m x5.8m = 389.76 m3
1 m3= 1000l
So capacity = 389.76x1000 = 389760 Litre
area of iron sheet required = total surface area of cistern
= 2(lb+bh+lh)
= 2(11.2x6 + 6x5.8 + 11.2x5.8)
= 2(166.96) m2
= 333.92 m2
capacity = 389.86 m3
area of sheet required = 333.92 m2
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Find the capacity of a rectangular cistern in litres whose dimensions ...
Capacity of the Cistern:
To find the capacity of the rectangular cistern, we need to multiply its dimensions: length, width, and height. Given that the dimensions are 11.2m, 6m, and 5.8m respectively, the capacity can be calculated as follows:
Capacity = Length × Width × Height
= 11.2m × 6m × 5.8m
= 387.84 cubic meters
Since 1 cubic meter is equal to 1000 liters, the capacity of the cistern can be converted to liters as follows:
Capacity in liters = Capacity in cubic meters × 1000
= 387.84 cubic meters × 1000
= 387,840 liters
Therefore, the capacity of the rectangular cistern is 387,840 liters.
Area of Iron Sheet:
To find the area of the iron sheet used to make the cistern, we need to calculate the surface area of the cistern. Since a rectangular cistern has six faces, each face contributes to the total surface area.
1. Top and Bottom Faces:
The top and bottom faces of the cistern are both rectangles with dimensions 11.2m and 6m. The area of each face can be calculated as follows:
Top/Bottom face area = Length × Width
= 11.2m × 6m
= 67.2 square meters
Since there are two identical faces (top and bottom), the total area contributed by the top and bottom faces is:
Total top/bottom face area = 2 × Top/Bottom face area
= 2 × 67.2 square meters
= 134.4 square meters
2. Side Faces:
The side faces of the cistern are rectangles with dimensions 11.2m, 5.8m, and 6m. The area of each face can be calculated as follows:
Side face area = Length × Height
= 11.2m × 5.8m
= 64.96 square meters
Since there are four identical side faces, the total area contributed by the side faces is:
Total side face area = 4 × Side face area
= 4 × 64.96 square meters
= 259.84 square meters
Total Surface Area:
To find the total surface area of the cistern, we need to sum up the areas of all the faces:
Total surface area = Total top/bottom face area + Total side face area
= 134.4 square meters + 259.84 square meters
= 394.24 square meters
Therefore, the area of the iron sheet used to make the cistern is 394.24 square meters.
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