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Total Surface Area of a Cuboid

In a cuboid, ...

Question

In a cuboid, if the sum of the lenghth of edges is represented by $S$ , the total surface area is represented by $T$ and the length of diagonal is represented by $D$ , then the value of $D$ is

\sqrt{\frac{S^{2}}{4} - T}

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\sqrt{\frac{S^{2}}{14} - T}

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\sqrt{\frac{S^{2}}{16} + T}

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\sqrt{\frac{S^{2}}{16} - T}

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Solution

The correct option is B $\sqrt{\frac{S^{2}}{16} - T}$
Sum of length of days = S = 4 (l +b + h )

TSA = t =2 (lb + bh +hl )

Length of diagonal = $D = \sqrt{l^{2} + b^{2} + h^{2}}$

$\sqrt{{(l + b + h)}^{2} - 2 (l b + b h + h l)}$

$\sqrt{S^{2} / 4^{2} - τ}$

$\sqrt{S^{2} / 16 - τ}$

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In a cuboid, if the sum of the lenghth of edges is represented by S, the total surface area is represented by T and the length of diagonal is represented by D, then the value of D is

The correct option is B √S216−TSum of length of days = S = 4 (l +b + h ) TSA = t =2 (lb + bh +hl ) Length of diagonal = D=√l2+b2+h2 √(l+b+h)2−2(lb+bh+hl) √S2/42−τ √S2/16−τ

In a cuboid, if the sum of the lenghth of edges is represented by $S$ , the total surface area is represented by $T$ and the length of diagonal is represented by $D$ , then the value of $D$ is

The correct option is B $\sqrt{\frac{S^{2}}{16} - T}$
Sum of length of days = S = 4 (l +b + h )

TSA = t =2 (lb + bh +hl )

Length of diagonal = $D = \sqrt{l^{2} + b^{2} + h^{2}}$

$\sqrt{{(l + b + h)}^{2} - 2 (l b + b h + h l)}$

$\sqrt{S^{2} / 4^{2} - τ}$

$\sqrt{S^{2} / 16 - τ}$