Question 68

The sum of the length, breadth and depth of a cuboid is 19 cm and its diagonal is $$5\sqrt{5}$$ cm. Its surface area is

Solution

Let length, breadth and height of cuboid is 'l', 'b' and 'h' respectively.

According to the question:

l + b + h = 19 ........ (1)

Diagonal of cuboid = $$\sqrt{l^{2} + b^{2} + h^{2}} = 5\sqrt{5}$$

$$l^{2} + b^{2} + h^{2} = 125$$ ...... (2)

We know that:

$$(l + b + h)^{2} = l^{2} + b^{2} + h^{2} + 2(lb + bh + hl)$$

From eqaution (1) and (2):

$$19^{2} = 125 + 2(lb + bh + hl)$$

$$2(lb + bh + hl) = 361 - 125 = 236$$

Surface area of cuboid = $$2(lb + bh + hl) = 236 cm^{2}$$

SRCC Inequalities QuestionsSRCC Number Systems QuestionsSRCC Geometry QuestionsSRCC Time, Distance and Work QuestionsSRCC Mensuration QuestionsSRCC Geometry QuestionsSRCC Functions, Graphs and Statistics QuestionsSRCC Averages, Ratio and Proportion QuestionsSRCC Averages, Ratio and Proportion QuestionsSRCC Quadratic Equations QuestionsSRCC Quadratic Equations QuestionsSRCC Averages Mixtures Alligations QuestionsSRCC Number Systems QuestionsSRCC Time And Work QuestionsSRCC Simple Interest Compound Interest QuestionsSRCC Venn Diagrams QuestionsSRCC Functions, Graphs and Statistics QuestionsSRCC Progressions and Series QuestionsSRCC Inequalities QuestionsSRCC Quadratic Equations QuestionsSRCC Data Sufficiency QuestionsSRCC Profit, Loss and Interest QuestionsSRCC Probability, Combinatorics QuestionsSRCC Probability, Combinatorics QuestionsSRCC Averages, Ratio and Proportion QuestionsSRCC Number Series QuestionsSRCC Progressions and Series QuestionsSRCC Data Sufficiency QuestionsSRCC Quadratic Equations QuestionsSRCC Coordinate Geometry QuestionsSRCC Profit And Loss QuestionsSRCC Venn Diagrams QuestionsSRCC Time, Distance and Work QuestionsSRCC Linear Equations QuestionsSRCC Progressions and Series QuestionsSRCC Remainders QuestionsSRCC Progressions and Series QuestionsSRCC Data Sufficiency QuestionsSRCC Functions, Graphs and Statistics QuestionsSRCC Time, Distance and Work QuestionsSRCC Time, Distance and Work QuestionsSRCC Functions, Graphs and Statistics QuestionsSRCC Number Systems QuestionsSRCC Venn Diagrams QuestionsSRCC Inequalities QuestionsSRCC Geometry QuestionsSRCC Averages QuestionsSRCC Logarithms, Surds and Indices QuestionsSRCC Venn Diagrams QuestionsSRCC Inequalities QuestionsSRCC Percentages QuestionsSRCC PGDBA Calculus QuestionsSRCC Logarithms, Surds and Indices QuestionsSRCC Linear Equations QuestionsSRCC Profit, Loss and Interest QuestionsSRCC Arithmetic QuestionsSRCC Linear Equations QuestionsSRCC Algebra QuestionsSRCC Profit, Loss and Interest QuestionsSRCC Probability, Combinatorics QuestionsSRCC Number Systems QuestionsSRCC Averages, Ratio and Proportion QuestionsSRCC Data Sufficiency QuestionsSRCC Logarithms, Surds and Indices QuestionsSRCC Time Speed Distance QuestionsSRCC Profit, Loss and Interest QuestionsSRCC Linear Equations QuestionsSRCC Logarithms, Surds and Indices QuestionsSRCC Geometry QuestionsSRCC Logarithms QuestionsSRCC Probability, Combinatorics Questions

SRCC Charts QuestionsSRCC Special Charts QuestionsSRCC Special Charts QuestionsSRCC Quant Based DI QuestionsSRCC Logical Reasoning QuestionsSRCC Table with Missing values QuestionsSRCC Innovation and Entrepreneurship QuestionsSRCC Charts QuestionsSRCC Puzzles QuestionsSRCC Maxima-Minima QuestionsSRCC Games and Tournamnents QuestionsSRCC DI with connected data sets QuestionsSRCC Charts QuestionsSRCC DI with connected data sets QuestionsSRCC Data Interpretation QuestionsSRCC Data Interpretation Basics QuestionsSRCC Puzzles QuestionsSRCC Scheduling QuestionsSRCC Quant Based DI QuestionsSRCC Logical Reasoning QuestionsSRCC Truth Lie Concept QuestionsSRCC Data change over a period QuestionsSRCC Quant Based LR QuestionsSRCC Quant Based LR QuestionsSRCC Logical Reasoning QuestionsSRCC 2D & 3D LR QuestionsSRCC Set Theory QuestionsSRCC Games and Tournamnents QuestionsSRCC Data Interpretation Basics QuestionsSRCC Data Interpretation QuestionsSRCC Scheduling QuestionsSRCC Data Interpretation Basics QuestionsSRCC Selection With Condition QuestionsSRCC Data Interpretation QuestionsSRCC Data Interpretation QuestionsSRCC Arrangement QuestionsSRCC Arrangement QuestionsSRCC Table with Missing values QuestionsSRCC Data change over a period QuestionsSRCC Venn Diagrams QuestionsSRCC Arrangement QuestionsSRCC DI Miscellaneous QuestionsSRCC Coins and Weights QuestionsSRCC Truth Lie Concept QuestionsSRCC Selection With Condition QuestionsSRCC Routes And Networks QuestionsSRCC Miscellaneous LR Questions

SRCC Para Summary QuestionsSRCC Para Jumbles QuestionsSRCC Reading Comprehension QuestionsSRCC Para Jumbles QuestionsSRCC Critical Reasoning QuestionsSRCC Vocabulary QuestionsSRCC Vocabulary QuestionsSRCC Reading Comprehension QuestionsSRCC Grammar and Sentence Correction QuestionsSRCC Grammar and Sentence Correction QuestionsSRCC Para Jumbles QuestionsSRCC Miscellaneous QuestionsSRCC Miscellaneous QuestionsSRCC Odd One Out QuestionsSRCC Critical Reasoning QuestionsSRCC Para Summary QuestionsSRCC Vocabulary QuestionsSRCC Grammar and Sentence Correction QuestionsSRCC Para Jumbles QuestionsSRCC Verbal Ability QuestionsSRCC Reading Comprehension QuestionsSRCC Para Summary QuestionsSRCC Vocabulary QuestionsSRCC Reading Comprehension QuestionsSRCC Grammar and Sentence Correction QuestionsSRCC Critical Reasoning Questions