Question

the surface area of a cuboid is 1300cm² if its length is 15cm and height is 20cm find its breadth​

Answer 1

$\frak{Given}\begin{cases}\sf{\;\;\; Length\; of\; cuboid\;is\;\bf{15\;cm}}\\\sf{\;\;\; Height\;of\; cuboid\;is\;\bf{20\;cm}}\\\sf{\;\;\;Surface\;area\;of\; cuboid\;is\;\bf{1300\;cm^2}}\end{cases}$

Need to find: The Breadth of cuboid.

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$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}$⠀⠀

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$\star\;\boxed{\sf{\pink{Surface\;area_{\:(cuboid)} = 2\Big\lgroup lb + bh + hl\Big\rgroup}}}$

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where,

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• l is length of the cuboid, b is breadth of the cuboid and h is the height of the cuboid. Surface area of cuboid is given that is 1300cm².

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Therefore,

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$:\implies\sf 1300 = 2\Big\lgroup 15 \times b + b \times 20 + 20 \times 15\Big\rgroup \\\\\\:\implies\sf 1300 = 2\Big\lgroup 15b + 20b + 300\Big\rgroup \\\\\\:\implies\sf \dfrac{1300}{2} = 15b + 20b + 300 \\\\\\:\implies\sf 650 = 15b + 20b + 300 \\\\\\:\implies\sf 650 - 300 = 35b \\\\\\:\implies\sf 350 = 35b \\\\\\:\implies\sf b = \cancel\dfrac{350}{35} \\\\\\:\implies{\underline{\boxed{\frak{\pink{b = 10\;cm}}}}}\;\bigstar$

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$\therefore\:\underline{\textsf{Breadth of the cuboid is \textbf{10 cm}}}.$

Answer 2

$\sf Given \: that \begin{cases} & \sf{Surface \: area \: of \: cuboid \: = \bf{1300 \: cm^{2}}} \\ & \sf{Length \: of \: cuboid \: = \bf{15 \: cm}} \\ & \sf{Height \: of \: cuboid \: = \bf{20 \: cm}} \end{cases}$

${\sf{\underline{To \: find}}}$

★ Breadth of the cuboid

${\sf{\underline{Solution}}}$

★ Breadth of the cuboid = 10 cm

${\sf{\underline{Using \: concept}}}$

★ Formula to find surface area of cuboid

${\sf{\underline{Using \: formula}}}$

★ Surface area of cuboid = 2(lb+bh+hl)

${\sf{\underline{Where,}}}$

★ l denotes length

★ b denotes breadth

★ h denotes height

${\sf{\underline{Here,}}}$

★ l is 15 cm

★ b is ? (Have to find)

★ h is 20 cm

★ Surface area is 1300 cm²

${\sf{\underline{Full \; Solution}}}$

~ Let's put the values according to the formula and at last we get our final result easily..!

➙ Surface area = 2(lb+bh+hl)

➙ 1300 = 2[15(b) + b(20) + 20(15)]

➙ 1300 = 2[15b + 20b + 300]

➙ 1300 = 2[35b + 300]

➙ 1300 = 70b + 600

➙ 1300 - 600 = 70b

➙ 700 = 70b

➙ 700/70 = b

➙ 70/7 = b

➙ 10 = b

➙ b = 10 cm

➙ Breadth = 10 cm

• Henceforth, 10 cm is the breadth of the given cuboid.

${\sf{\underline{Additional \; knowledge}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto TSA \: of \: cuboid \: = \: 2(l \times b + b \times h + l \times h)}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto LSA \: of \: cuboid \: = \: 2h(l+b)}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Volume \: of \: cuboid \: = \: L \times B \times H}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Diagonal \: of \: cuboid \: = \: \sqrt 3l}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Perimeter \: of \: cuboid \: = \: 12 \times Sides}}}$