Sum of the length,width and depth of a cuboid | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the length,width,and depth of the cuboid be $l$,$b$,and $h$ respectively.Given that the sum of dimensions is $l + b + h = s$.The diagonal of t

Vedclass · Accepted Answer

$s^{2}-d^{2}$

Vedclass · Answer

(C) Let the length,width,and depth of the cuboid be $l$,$b$,and $h$ respectively.Given that the sum of dimensions is $l + b + h = s$.The diagonal of the cuboid is given by $\sqrt{l^{2} + b^{2} + h^{2}} = d$,which implies $l^{2} + b^{2} + h^{2} = d^{2}$.We know the algebraic identity: $(l + b + h)^{2} = l^{2} + b^{2} + h^{2} + 2(lb + bh + hl)$.Substituting the given values,we get: $s^{2} = d^{2} + 2(lb + bh + hl)$.The surface area of a cuboid is given by $2(lb + bh + hl)$.Therefore,$2(lb + bh + hl) = s^{2} - d^{2}$.Thus,the surface area is $s^{2} - d^{2}$.

Sum of the length,width and depth of a cuboid is $s$ and its diagonal is $d$. Its surface area is

Similar Questions

$A$ cube of lead with edges measuring $6\, cm$ each is melted and recasted into $27$ equal cubes. The length of the edge of the new cube is.......$cm$

Assume that a drop of water is spherical and its diameter is $\frac{1}{10} \text{ cm}$. $A$ conical glass has a height equal to the diameter of its rim. If $32,000$ drops of water fill the glass completely,then the height of the glass (in $\text{cm}$) is:

$A$ metallic sheet is of rectangular shape with dimensions $48\, m \times 36\, m$. From each of its corners, a square is cut off so as to make an open box. If the length of the side of the square is $8\, m$, the volume of the box (in $m^3$) is:

$A$ cylindrical jar of diameter $24\, cm$ contains water to a height of $30\, cm$. $A$ spherical steel ball is dropped into the jar and the level of the water rises by $67.5\, mm$. The diameter of the ball is......$cm$.

Find the weight of a hollow cylindrical lead pipe $28\, cm$ long and $0.5\, cm$ thick. Its internal diameter is $8\, cm$. (in $kg$) (Weight of $1\, cm^3$ of lead is $11.4\, g$,$\pi = \frac{22}{7}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module