CLAT 2020 Quantitative Techniques: Mensuration

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?

Dimensions

Sr.No.	Object	Length	Breadth	Height
1	Room	18 feet	12 feet	12 feet
2	Bed	3.5 feet	6 feet	3 feet
3	Table	3 feet	4 feet	4 feet
4	Chair	2 feet	2.5 feet	4 feet
5	Books	12 inches	6 inches	3 inches

What is the area of the table which is uncovered by any of the objects?

Let's expand the Dimensions table and add 2 more columns, Surface Area, and Volume.
Note: 1 Foot = 12 inches

DimensionsExpanded

Sr.No	Object	Length(l)	Breadth(b)	Height(h)	Floor Surface Area (l*b) in square feet	Volume (l*b*h) in cubic feet
1	Room	18	12	12	216	2592
2	Bed	3.5	6	3	21	63
3	Table	3	4	4	12	48
4	Chair	2	2.5	4	5	20
5	Books	1	0.5	0.25	0.5	0.125

The area of the table in sq. inches is 12 * (12 * 12) = 1728 sq. inches
Area of 1 book in sq. inches = 0.5 * (12 * 12) = 72 sq. inches
Area of the lamp, whose radius is 3.5 inches = \(\frac{22}{7} \) (3.5)² =  \(\frac{22}{7} \) ( \(\frac{7}{2} \) )² = 38.5 sq. inches

There are 3 books on the table and a lamp.
The uncovered area of the table = 1728 - 3(72) - 38.5 =  1473.5 (approx. since we considered pi as   \(\frac{22}{7} \))

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