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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?
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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.
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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).
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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.

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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?
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