All Courses
Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity Get the App Login Join for Free
Sign in Open App
CAT Exam  >  CAT Questions  >   Length and breadth of a cuboid are increased... Start Learning for Free
SaveJoin the Discussion on the App
Length and breadth of a cuboid are increased by 30% and 70 % respectively and height is decreased by 20 %. What is the ratio %age change in surface area to percentage change in volume?
  • a)
    45.6 %
  • b)
    98 %
  • c)
    91.2 %
  • d)
    Cannot be determined
Correct answer is option 'D'. Can you explain this answer?
FREE This question is part of
Download PDF Attempt Test
Download PDF Attempt this Test
Most Upvoted Answer
Length and breadth of a cuboid are increased by 30% and 70 % respecti...
Given:
The length and breadth of a cuboid are increased by 30% and 70% respectively.
The height is decreased by 20%.

To find:
The ratio of the percentage change in surface area to the percentage change in volume.

Solution:

Let's assume the original length, breadth, and height of the cuboid to be L, B, and H respectively.

After the given changes, the new length, breadth, and height will be:
New length = L + 0.3L = 1.3L
New breadth = B + 0.7B = 1.7B
New height = H - 0.2H = 0.8H

Calculating the new surface area:
The surface area of a cuboid is given by:
2(LB + BH + HL)

The new surface area (SA') will be:
2(1.3L * 1.7B + 1.7B * 0.8H + 0.8H * 1.3L)
= 2(2.21LB + 1.36BH + 1.04HL)
= 4.42LB + 2.72BH + 2.08HL

The percentage change in surface area can be calculated as:
((SA' - SA) / SA) * 100

Calculating the new volume:
The volume of a cuboid is given by:
LBH

The new volume (V') will be:
1.3L * 1.7B * 0.8H
= 1.664LBH

The percentage change in volume can be calculated as:
((V' - V) / V) * 100

Calculating the ratio:
The ratio of the percentage change in surface area to the percentage change in volume will be:
((SA' - SA) / SA) / ((V' - V) / V)
= ((4.42LB + 2.72BH + 2.08HL - LBH) / (LBH)) / ((1.664LBH - LBH) / LBH)

Simplifying further, we get:
= (3.42LB + 2.72BH + 2.08HL) / (0.664LB)
= (3.42 + 2.72(B/H) + 2.08(L/H)) / 0.664

Conclusion:
The ratio of the percentage change in surface area to the percentage change in volume cannot be determined without knowing the specific values of B/H and L/H. Hence, the correct answer is option D) Cannot be determined.
Free Test
FREE
Start Free Test
Start Free Test
Community Answer
Length and breadth of a cuboid are increased by 30% and 70 % respecti...
S.A. ∝ lb + bh + hl
After increasing l by 30% new l = 1.3 l
After increasing b by 70% new b = 1.7 b
After decreasing h by 20% new h = 0.8 h
New SA ∝ (1.3 × 1.7lb + 1.7 × 0.8bh + 0.6h × 1.3l)
New volume ∝ (1.3 × 1.7 × 0.8 lbh )
Percentage change cannot be determined, because while calculating the change, coefficients of lb, bh, and hl are different.
Hence, the correct option is (d).
Attention CAT Students!
To make sure you are not studying endlessly, EduRev has designed CAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CAT.
< Previous Question Next Question >
Explore Courses for CAT exam

Similar CAT Doubts

Each question is followed by two statements, A and B. Answer each question using the following instructions:Mark option (1) if the question can be answered by using statement A alone but not by using statement B alone.Mark option (2) if the question can be answered by using statement B alone but not by using statement A alone.Mark option (3) if the question can be answered by using either statement alone.Mark option (4) if the question can be answered by using both the statements together but not by either of the statements alone.Mark option (5) if the question cannot be answered on the basis of the two statements.Q. If the breadth of a rectangle is increased by 2 units and the length is decreased by 3 units, the area is unchanged. What is the area of the rectangle?A. If the breadth is decreased by 1 unit and the length is increased by 3 units, the area remains the same.B. If the breadth is increased by 1 unit and the length is increased by 2 units, the area gets doubled.

Top Courses for CATView all

Top Courses for CAT

Length and breadth of a cuboid are increased by 30% and 70 % respectively and height is decreased by 20 %. What is the ratio %age change in surface area to percentage change in volume?a)45.6 %b)98 %c)91.2 %d)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer?
Question Description
Length and breadth of a cuboid are increased by 30% and 70 % respectively and height is decreased by 20 %. What is the ratio %age change in surface area to percentage change in volume?a)45.6 %b)98 %c)91.2 %d)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Length and breadth of a cuboid are increased by 30% and 70 % respectively and height is decreased by 20 %. What is the ratio %age change in surface area to percentage change in volume?a)45.6 %b)98 %c)91.2 %d)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Length and breadth of a cuboid are increased by 30% and 70 % respectively and height is decreased by 20 %. What is the ratio %age change in surface area to percentage change in volume?a)45.6 %b)98 %c)91.2 %d)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer?.
Solutions for Length and breadth of a cuboid are increased by 30% and 70 % respectively and height is decreased by 20 %. What is the ratio %age change in surface area to percentage change in volume?a)45.6 %b)98 %c)91.2 %d)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT. Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of Length and breadth of a cuboid are increased by 30% and 70 % respectively and height is decreased by 20 %. What is the ratio %age change in surface area to percentage change in volume?a)45.6 %b)98 %c)91.2 %d)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Length and breadth of a cuboid are increased by 30% and 70 % respectively and height is decreased by 20 %. What is the ratio %age change in surface area to percentage change in volume?a)45.6 %b)98 %c)91.2 %d)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for Length and breadth of a cuboid are increased by 30% and 70 % respectively and height is decreased by 20 %. What is the ratio %age change in surface area to percentage change in volume?a)45.6 %b)98 %c)91.2 %d)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of Length and breadth of a cuboid are increased by 30% and 70 % respectively and height is decreased by 20 %. What is the ratio %age change in surface area to percentage change in volume?a)45.6 %b)98 %c)91.2 %d)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Length and breadth of a cuboid are increased by 30% and 70 % respectively and height is decreased by 20 %. What is the ratio %age change in surface area to percentage change in volume?a)45.6 %b)98 %c)91.2 %d)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice CAT tests.
Explore Courses for CAT exam

Top Courses for CAT

Explore Courses

Suggested Free Tests

Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Get App
© EduRev
Education Revolution
Signup to see your scores go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup