# the sum of the length, breadth and height of a cuboid is 6√3cm and the length of its diagonal is 2√3cm. the total surface area of the cuboid is

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## The sum of length, breadth and height of a cuboid is 38 cm and the lengths of its diagonal is 22 cm . Find the total surface area of the cuboid (in cm^2 ).

Click here👆to get an answer to your question ✍️ The sum of length, breadth and height of a cuboid is 38 cm and the lengths of its diagonal is 22 cm . Find the total surface area of the cuboid (in cm^2 ).

The sum of length, breadth and height of a cuboid is 38 cm and the lengths of its diagonal is 22 cm. Find the total surface area of the cuboid (in cmQuestion 2 ). Medium Open in App

Updated on : 2022-09-05

Solution Verified by Toppr

Correct option is A)

Let be length =l, breadth =b, height =hAccording to question,

l+b+h=38

Squaring both side, we get,

(l+b+h) 2 =38 2 ⇒l 2 +b 2 +h 2

+2lb+2bh+2lh=1444 .....(i)

Diagonal of cuboid =

l 2 +b 2 +h 2 l 2 +b 2 +h 2 =22

Squaring both side, we get

l 2 +b 2 +h 2 =22×22=484 Put the value l 2 +b 2 +h 2

in equation (i), we get

484+2(lb+bh+lh)=1444

⇒2(lb+bh+lh)=1444−484

∴ Total surface area of cuboid =960 cm

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## The sum of the length, breadth and the height of a cuboid is 5sqrt(3) cm and length of its diagonal is 3sqrt(5) cm. Find the total surface area of the cuboid.

(i) Use suitable algebraic identity to find the LSA of the cuboid. (ii) l+b+h=5sqrt(3 ) and l^(2)+b^(2)+h^(2)=3sqrt(5). (iii) Square the first equation and evaluate 2(lb+bh+hl).

Home > English > Class 10 > Maths > Chapter > Mensuration >

The sum of the length, breadth...

The sum of the length, breadth and the height of a cuboid is

5 3 – √ 53

cm and length of its diagonal is

3 5 – √ 35

cm. Find the total surface area of the cuboid.

Updated On: 27-06-2022

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Text Solution Open Answer in App A 30c m 2 30cm2 B 20c m 2 20cm2 C 15c m 2 15cm2 D 18c m 2 18cm2 Answer

The correct Answer is C

Solution

(i) Use suitable algebraic identity to find the LSA of the cuboid.

(ii) l+b+h=5 3 – √ and l 2 + b 2 + h 2 =3 5 – √ .

l+b+h=53andl2+b2+h2=35.

(iii) Square the first equation and evaluate

2(lb+bh+hl) 2(lb+bh+hl) . Answer

Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.

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## [Solved] The sum of length, breadth and height of a cuboid is 20 cm.

Given- Sum of length, breadth and height = 20 cm Length of the diagonal = 12 cm Formula Used- Length of diagonal of a cuboid = &radi

Home Quantitative Aptitude Mensuration Solid Figures Cuboid

## Question

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## The sum of length, breadth and height of a cuboid is 20 cm. If the length of the diagonal is 12 cm, then find the total surface area of cuboid.

This question was previously asked in

SSC CGL Tier 2 Quant Previous Paper 3 (Held On: 18 November 2020)

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364 cm2 264 cm2 356 cm2 256 cm2

## Answer (Detailed Solution Below)

Option 4 : 256 cm2 Crack SSC with

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## Detailed Solution

Download Solution PDF

**Given-**

Sum of length, breadth and height = 20 cm

Length of the diagonal = 12 cm

**Formula Used-**

Length of diagonal of a cuboid = √(l2 + b2 + h2) [where l = length, b = breadth and h = height]

Total Surface Area of cuboid = 2(lb + bh + hl) [where l = length, b = breadth and h = height]

(l + b + h)2 = l2 + b2 + h2 + 2(lb + bh + hl)

**Calculation-**

According to condition -

√(l2 + b2 + h2) = 12

⇒ l2 + b2 + h2 = 144

Again, l + b + h = 20

⇒ (l + b + h)2 = 400

⇒ l2 + b2 + h2 + 2(lb + bh + hl) = 400

⇒ 2(lb + bh + hl) = 400 - 144

⇒ 2(lb + bh + hl) = 256

∴ The total surface area of cuboid = 256 cm2

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