Question

A cuboid has length 30cm and breadth 25cm. If its total surface is double the lateral surface area.

Answer 1

$\huge\bold{SOLUTION}$
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Given:-

$L$ = 30cm

$B$ = 25cm

T.S.A of Cuboid = 2×(LSA of Cuboid)
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Find:-

Height = ?

T.S.A = ?

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T.S.A of cuboid = 2×(LSA of cuboid)

2(LB + BH + HL) = 2×[2(L + B)×H]

2 cancels from both sides, we get

LB + BH + HL = 2H×(L + B)

LB + BH + HL = 2HL + 2BH

LB = HL + BH

LB = H(L + B)

H = $\dfrac{L×B}{L+B}$

H = $\dfrac{30×25}{30+25}$

H = $\dfrac{750}{55}$

H = $\dfrac{150}{11}$

H = 13.6cm
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TSA of Cuboid = 2(LB + BH + HL)

=> 2(30 × 25 + 25 × 13.6 + 13.6 × 30)

=> 2(750 + 340 + 408)

=> 2(1498)

=> 2996cm²
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