The sum of the length, breadth and depth of a cuboid is 19 cm and its

1.	The sum of the length, breadth and depth of a cuboid is 19 cm and its diagonal is 5√5 cm. Its surface area isA. 361 cm2B. 125 cm2C. 236 cm2D. 486 cm2
Answer» Correct option is C. 236 cm² Given, Sum of length ,breadth, height of cuboid = 19 cm Diagonal of cuboid = 5√5 cm \(=\sqrt{l^2+b^2+h^2}\) = 5√5 (Squaring both side) = l² + b²+ h² = 125......(i) \(\therefore\)(l + b + h)² = l² + b² + h² +2(lb + bh + hl) by formula Putting values … = 19² = 125 + 2(lb + bh + hl) = 2(lb + bh + hl) = 361 - 125 = 236 = surface area of cuboid = 236 cm²

The sum of the length, breadth and depth of a cuboid is 19 cm and its diagonal is 5√5 cm. Its surface area isA. 361 cm2B. 125 cm2C. 236 cm2D. 486 cm2

Answer»

Correct option is C. 236 cm²

Given,

Sum of length ,breadth, height of cuboid = 19 cm

Diagonal of cuboid = 5√5 cm

\(=\sqrt{l^2+b^2+h^2}\) = 5√5

(Squaring both side)

= l² + b²+ h² = 125......(i)

\(\therefore\)(l + b + h)² = l² + b² + h² +2(lb + bh + hl) by formula

Putting values …

= 19² = 125 + 2(lb + bh + hl)

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

= surface area of cuboid = 236 cm²