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The Sum of the Length, Breadth and Depth of a Cuboid is 19 Cm and Its Diagonal is 5 √ 5 Cm. Its Surface Area is - Mathematics

MCQ

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

Options

  •  361 cm2

  • 125 cm2

  •  236 cm2

  • 486 cm2

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Solution

Let,

l → Length of the cuboid

b → Breadth of the cuboid

h → Height of the cuboid

We have,

 l + b + h = 19 cm , diagonal of the cuboid

`( sqrt(l^2 + b^2 +h^2)) = 5 sqrt(5) cm `

We are asked to find the surface area

So, the surface area,

= 2 (lb + bh + hl )

= (l + b +h )- ( l+ b2 + h2

`=(l + b+ h) - ( sqrt (l^2 + b^2 + h^2 ))^2`

`=19^2 - (5sqrt(5))^2`

=361-125

=236 cm2

Thus, the surface area is 236 cm2

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 18 Surface Areas and Volume of a Cuboid and Cube
Q 20 | Page 36
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