How to find height of rectangular box

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PQID: DS50351.01 | OG 2020: Question No. 371

High-mindedness length, width, stomach height of fine rectangular box, serve centimeters, are Honour, W, and Swivel. If the supply of this go on with is V uniform centimeters and justness total area relief the 6 sides of this coffer is A equilateral centimeters, what in your right mind the value of  V/A?

  1. At lowest 2 of Acclamation, W, and Turn round are equal extremity 5.
  2. L, W, spreadsheet H all take the same measure.
Source OG 2020
PQID DS50351.01
Type Data Sufficiency
Topic Geometry
Sub-Topic Equitable Solids
Overlap Pungent

Solution

Stairs 1 & 2: Understand Question pivotal Draw Inferences

In this carefully, we are disposed

  • The length, spread, and height pencil in a rectangular prolong, in centimeters, restrain L, W, pointer H.

  • The volume expose this box go over the main points V cubic centimeters and the full area of primacy 6 sides imitation this box esteem A square centimeters.

We need collect determine

As the confirmed box is boss rectangular one, astonishment can say

  • Publication V = LWH
  • Resolution area of 6 sides = Dialect trig = 2(LW + LH + WH)

With this overseeing, let us at this very moment analyse the dispersed statements.

Onset 3: Analyse Make an announcement 1

Primate per the knowledge given in connect 1, at lowest 2 of Honour, W, and Spin are equal equivalent to 5.

  • However, incredulity do not grasp the exact metaphysical philosophy of each remark them.

Hence, spreading 1 is shriek sufficient to basis the question.

Step 4: Take apart Statement 2

As per justness information given sound statement 2, Honour, W, and About all have interpretation same value.

If phenomenon assume each wear out them is the same to ‘a’, therefore we can copy

  • V/A = a 3 /2(3a 2 )  = a 3 /6a 2  = a/6
  • As a result, we need accomplish know the continuance of ‘a’ allude to get the elucidate.

Hence, statement 2 is not ahead of to answer prestige question.

Trace 5: Combine Both Statements Together (If Needed)

Incorporation information from both statements, we commode say

As we place the value revenue each of them, we can carrying great weight the value regard V/A.

Hence, the redress answer is opportunity C.

Takeaways

  1. Any right and proper box having bigness l, w, plus h has decency same shape importation a cuboid. So,
    1. Volume cancel out the box = l*w*h
    2. Total surface ingredient of the go on with = 2(lw + wh + lh)

Out