IPMAT Rohtak 2019 (QA) - A room has floor size of 15 x 6 sq.cm. What is the height of the room, if the sum of the areas of the base and roof is equal to the sum of the areas of the four walls? | PYQs + Solutions | AfterBoards
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IPMAT Rohtak 2019

Geometry
>
Solids

Medium

A room has floor size of 15×615 \times 6 sq.cm. What is the height of the room, if the sum of the areas of the base and roof is equal to the sum of the areas of the four walls?

Correct Option: 3
Floor size = 15×615 \times 6 sq.cm \newline Let height of room be hh cm
Area of base and roof = 2(15×6)2(15 \times 6) = 2(90)2(90) = 180180 sq.cm
Area of walls: \newline - Front and back walls = 2(15×h)2(15 \times h) = 30h30h sq.cm \newline - Side walls = 2(6×h)2(6 \times h) = 12h12h sq.cm \newline - Total wall area = 30h+12h30h + 12h = 42h42h sq.cm
Given that sum of base and roof area = sum of wall areas: \newline 180=42h180 = 42h \newline h=18042h = \frac{180}{42}
h=4.29h = 4.29 cm
Therefore, the height of the room is 4.294.29 cm.

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