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# 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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### Mohammed

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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 cm

Question 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 =h

According 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

2 Video Explanation 19 1

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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

## 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

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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## More Solid Figures Questions

Q1. The ratio of radii of a cylinder to a that of a cone is 1 : 2. if their heights are equal, find the ratio of their volumesQ2. Find the weight of a cylindrical metal container with base radius 10.5 cm and height 6 m where the weight of 1 cm3 of metal is 5 grams.Q3. A right circular cone is surmounted on a hemisphere. Base radius of the cone is equal to radius of the hemisphere. The diameter of the hemisphere is 12 cm while the height of the cone is 8 cm. Find the cost of painting the compound object if it costs ₹25 to paint π cm2.Q4. The radius of the base of a conical tent is 9 m and its height is 12 m, find the cost of the material needed to make it if it costs ₹100 per π m2.Q5. The outer radius of a spherical shell is 9 cm and the thickness of the shell is 1 cm. Find the volume of the metal used for the shell (in cubic cm).

(Useπ=227)

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Mohammed 15 day ago

Guys, does anyone know the answer?