A room having the dimensions as mentioned in the chart below has a table, a bed and a chair. There are three books kept on the table (side by side) and also a lamp having radius, 3.5 inch. Now, on the basis of information given below answer the following?
Question: 1
What would be the area of the room which is not covered by any object as mentioned above?
This question asks for the area of the room's floor that is left uncovered once the footprints of the bed, table, and chair are taken out. The lamp and books sit on top of the table, so they do not use up any extra floor space of their own.
176.5 sq. ft.: This is close to the correct value but falls slightly short of the figure obtained when all three footprints are subtracted correctly.
178 sq. ft.: The room's total floor area is 18 feet by 12 feet, which is 216 square feet. The bed takes up 3.5 by 6 feet, which is 21 square feet. The table takes up 3 by 4 feet, which is 12 square feet. The chair takes up 2 by 2.5 feet, which is 5 square feet. Subtracting all three from the room's area gives 216 minus 21 minus 12 minus 5, which is 178 square feet. This matches the computed figure exactly.
367 sq. ft.: This is larger than the room's own total floor area of 216 square feet, so it cannot be correct under any reasonable subtraction.
245.5 sq. ft.: This also exceeds the room's total area of 216 square feet, which rules it out immediately since the uncovered area can never be more than the room itself.
Subtracting the floor footprints of the bed, table, and chair from the total floor area of the room leaves the space not covered by any object.
Therefore, the correct answer is 178 sq. ft..
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Question: 2
What is the area of the table which is uncovered by any of the objects?
This question asks for the part of the table's surface that is left free once the three books and the lamp are placed on it. We need to convert the table's dimensions to inches to match the units used for the books and the lamp.
1656 sq. inch: This does not match the figure obtained once the books and the circular lamp base are both subtracted correctly from the table's area.
1617.52 sq. inch: This is close to the correct value but does not account for the full area used by all three books together.
1473.52 sq. inch: The table measures 3 feet by 4 feet, which is 36 inches by 48 inches, giving a total area of 36 times 48, or 1728 square inches. Each book measures 12 inches by 6 inches, so one book covers 72 square inches, and three books placed side by side cover 3 times 72, which is 216 square inches. The lamp has a radius of 3.5 inches, so its circular base covers pi times 3.5 squared, which is about 38.48 square inches. Subtracting both the books and the lamp from the table's area gives 1728 minus 216 minus 38.48, which is 1473.52 square inches. This matches the calculation exactly.
1512 sq. inch: This figure would only arise if the lamp's area were ignored altogether, which leaves out one of the objects the question asks us to account for.
Converting the table to the same inch units as the books and lamp, then subtracting both footprints, gives the free area of the table's surface.
Therefore, the correct answer is 1473.52 sq. inch.
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Question: 3
How many tables are required to cover the floor surface of the room completely?
This question asks how many tables, placed flat on the floor, would be needed to completely cover the room's floor area, using each object's own footprint.
18: The room's floor area is 18 feet by 12 feet, which is 216 square feet. Each table has a footprint of 3 feet by 4 feet, which is 12 square feet. Dividing the room's area by one table's area gives 216 divided by 12, which is exactly 18. This matches the calculation precisely, since the table's footprint divides the room's area with no remainder.
11: This is too low a count. Multiplying 11 tables by 12 square feet each gives only 132 square feet, well short of the room's 216 square feet.
21: This overshoots the requirement. Multiplying 21 tables by 12 square feet each gives 252 square feet, more than the room's actual floor area.
Data inadequate: Since both the room's dimensions and the table's dimensions are given directly in the chart, there is enough information to calculate an exact number, so this option does not apply.
Dividing the room's total floor area by a single table's footprint gives the exact number of tables needed to cover it completely.
Therefore, the correct answer is 18.
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Question: 4
If the entire room is to be filled by books having same dimensions as lying on the table then how many books are required.
This question is different from the earlier floor area ones, since filling the entire room means comparing volumes, not just floor footprints. We need the room's full volume and one book's full volume, converted to the same unit.
2,00,736: This figure is too large by a factor of ten and does not match the correct volume based calculation.
20,736: The room's volume is 18 feet by 12 feet by 12 feet, which is 2592 cubic feet. One book measures 12 inches by 6 inches by 3 inches, giving a volume of 216 cubic inches. Since 1 cubic foot equals 1728 cubic inches, one book's volume in cubic feet is 216 divided by 1728, which is 0.125 cubic feet, or one eighth of a cubic foot. Dividing the room's volume by one book's volume gives 2592 divided by 0.125, which is exactly 20,736. This matches the computed figure precisely.
11,736: This does not correspond to a consistent volume based division of the room by a single book, and is too low to fill the entire room.
17,522: This is closer to the correct order of magnitude but does not match the exact division of 2592 cubic feet by 0.125 cubic feet.
Converting both the room and the book to the same volume unit, then dividing, gives the exact number of books needed to fill the room completely.
Therefore, the correct answer is 20,736.
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Question: 5
How many chairs can be put inside the room so as to cover the entire floor area of the room?
This question asks how many chairs, placed on the floor, can fit inside the room based purely on floor footprint, using the room's and the chair's given dimensions.
40: This undercounts the room's capacity. Multiplying 40 chairs by 5 square feet each gives only 200 square feet, which leaves floor space unused.
21: This is far too low, covering only 105 square feet of the room's 216 square feet, leaving well over half the floor unaccounted for.
43: Each chair has a footprint of 2 feet by 2.5 feet, which is 5 square feet. The room's floor area is 216 square feet. Dividing 216 by 5 gives 43.2. Since a fraction of a chair cannot physically be placed, we take the whole number, which is 43 chairs, using 215 square feet and leaving a sliver of unused space that is not enough for one more whole chair. This matches the number of chairs that can actually fit.
18: This is far too small a number for the room's floor area, since 18 chairs at 5 square feet each would only use 90 square feet, leaving most of the room's floor empty.
Dividing the room's floor area by a single chair's footprint, and rounding down to a whole number of chairs, gives the maximum count that fits.
