Question

what is the length of a cuboid having breadth and height equal to 4cm and 6cm respectively,and the total surface area of 148cm²​

Answer 1

Answer:

The length of the cuboid is 5 cm.

Step-by-step explanation:

The total surface area of a cuboid with length  $l$, breadth $b$ and height $h$ is given by the formula,

$Total\ surface\ area(TSA)=2(lb+bh+lh)$

Given that, the cuboid has a breadth of 4 cm, a height of 6 cm, and a total surface area of 148 $cm^2$. Substitute the values in the formula, we get,

$148=2(l\times 4+4\times 6+l\times 6)\\\\\implies 148= 2(4l+24+6l) \\\\\implies \dfrac{148}{2}=10l+24\\\\ \implies 74= 10l+24\\\\\implies 10 l =74-24=50\\\\\implies l= 5$

So the length of the cuboid is 5 cm.

Answer 2

$\bf \bigstar \: \underline{Information \: provided \: in \: question:}$

$\rm \star \:Breadth \: of \: Cuboid = 4 \: cm$

$\rm \star \: Height \: of \: Cuboid = 6\: cm$

$\rm \star \: Surface \: area \: of \: Cuboid = 148 \: {cm}^{2}$

$\bf \bigstar \: \underline{What \: we \: \: have \: to \: calculate:}$

$\rm \star \: Length\: of \: Cuboid :$

$\bf \bigstar \: \underline{We \: know \: that} :$

$\rm \implies\: Surface \: area \: of \: Cuboid :$

$\rm \implies {\: 2 \times (l \: b + b \: h + l \: h)}$

$\bf \bigstar \: \underline{Consider} :$

$\rm{Assume \: that \: length \: be \: x}$

$\bf \bigstar \: \underline{So} :$

$\rm \implies \: 148 \: {cm}^{2} = 2 \times (4 \: x + 6 \: x + 6 \times 4)$

$\rm \implies \: 148 \: {cm}^{2} = 2 \times (10 \: x + 24)$

$\rm \implies \: 148 \: {cm}^{2} = (20 \: x + 48)$

$\rm \implies \: 20\: x = 148 - 48$

$\rm \implies \: 20\: x = 100$

$\rm \implies \:x = \dfrac{100}{20}$

$\rm \implies \:x =5 \: cm$

$\bf \bigstar \: \underline{Therefore} :$

$\rm{ \therefore Length \: of \: Cuboid \: is \: 5 cm }</p><p>$

$\bf \bigstar \: \underline{Verification}:$

$\rm \implies\: Surface \: area \: of \: Cuboid :$

$\rm \implies {\: 2 \times (l \: b + b \: h + l \: h)}$

$\rm \implies \: 148 \: {cm}^{2} = 2 \times (4 \times 5 + 6 \times 5+ 6 \times 4)$

$\rm \implies \: 148 \: {cm}^{2} = 2 \times (20 + 30 + 24)$

$\rm \implies \: 148 \: {cm}^{2} = 2 \times (74)$

$\rm \implies \boxed{ \: 148 \: {cm}^{2} = 148 \: {cm}^{2}}$

$\bf \bigstar \: \underline{Hence \: Verified}:$