The length of cuboid is two times of its breadth and four times of its height. If the volume of cuboid is 64m³, find its total surface of ar

Question

The length of cuboid is two times of its breadth and four times of its height. If the volume of cuboid is 64m³, find its total surface of area.

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Quinn 3 weeks 2021-11-07T09:13:05+00:00 2 Answers 0 views 0

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    0
    2021-11-07T09:14:07+00:00

    Answer

    The total surface area of the cuboid is 112m²

    \bf\large\underline{Given}

    • The length of the cuboid is 2 times of its breadth and 4 times of its height

    \bf\large\underline{To \ Find}

    • The total surface area of the cuboid

    \bf\large\underline{Formula \ to \ be \ used}

     \bullet  \:  \:  \sf Volume \: of \:cuboid = l \times h \times b  \\   \bullet \: \: \sf Surface \: area = 2(lh + lb + hb) \\ \sf where  : \\  \sf l \longrightarrow \: length \: of \: cuboid \\  \sf h\longrightarrow  \:  \: height   of \: cuboid \\  \sf b \longrightarrow breadth \: of \: cuboid

    \bf\large\underline{Solution}

    We are given ,

    The length is 2 times the breadth

    \sf\implies l = 2b \\\\ \sf\implies b = \dfrac{l}{2}

    And again ,

    The length is 4 times the height

    \sf \implies l = 4h \\\\ \sf\implies h = \dfrac{l}{4}

    Also we are given ,

     \sf Volume \: of \: cuboid = 64m {}^{3}  \\  \\  \implies \sf l \times h \times b = 64 {m}^{3}  \\  \\  \implies  \sf l \times  \frac{l}{2}  \times  \frac{l}{4}  = 64 {m}^{3}   \\  \\  \sf \implies l {}^{3}  = 64x8 {m}^{3}  \\  \\  \sf \implies l {}^{3}  = 4^{3}  \times 2^{3} m ^{3}  \\  \\   \sf\implies l ^{3}  = ( {8m)}^{3}  \\  \\  \sf \implies l = 8m

    Therefore , the length of the cuboid is 8m

    Thus the breadth and height is

     \sf h =  \dfrac{8m}{2}  \:  \: and \:  \:  \: b =  \dfrac{8m}{4}  \\  \\  \sf \implies h = 4m \:  \: and \:  \:  \implies b = 2m

    Now , calculating the surface area :

     \sf S.A \: of \: cuboid = 2(8 \times 4+ 8 \times 2 + 4 \times 2) \\  \\  \sf \implies S.A  \: of \: cuboid = 2(32 + 16 + 8) \\  \\  \sf \implies S.A  \: of \: cuboid =2 \times 56 \\  \\  \sf  \implies S.A  \: of \: cuboid = 112m {}^{2}

    Ther , required surface area of the cuboid is 112m²

    0
    2021-11-07T09:14:10+00:00

    \large\bf Given:-

    • The length of cuboid is two times it’s breadth.

    • The length of cuboid is four times it’s height.

    • Volume of cuboid = 64m³

    \large\bf To\:Find

    • The total surface area of the cuboid

    \large \bf Solution

    Let the length of the cuboid be x

    Given length is 2 times its breadth

    \rm\implies l =   2b

     \rm\implies b =  \dfrac{l}{2}

    \rm\implies b =  \dfrac{x}{2}

    Given, length is 4 times its height

    \rm\implies l =   4h

    \rm\implies h =    \dfrac{l}{4}

    \rm\implies h =    \dfrac{x}{4}

    Volume of cuboid = l × b × h = 64cm³

    \rm\implies x \times  \dfrac{x}{2}  \times  \dfrac{x}{4}  = 64

    \rm\implies   \dfrac{ { \:  \: x}^{3} }{8}  = 64

    \rm\implies   { { \:  \: x}^{3} } = 64 \times 8

     \rm\implies   { { \:  \: x}^{3} } = 512

    \rm\implies  x =  \sqrt[3]{512}

    \rm\implies  x =  8

     \rm Length = x = 8m

    \rm Breadth =  \dfrac{x}{2}  =  \dfrac{8}{2}  = 4m

     \rm height=  \dfrac{x}{4}  =  \dfrac{8}{4}  = 2m

    Now;

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

    \rm  \longrightarrow2 \{(8 \times 4 )+ (4 \times 2) + (2 \times 8) \}

    \rm  \longrightarrow2 (32+ 8+ 16)

    \rm  \longrightarrow2 (56)

     \rm  \longrightarrow112

    Therefore:-

    \boxed{  \bf \therefore Surface \: area \: of \: cuboid \:  = 112 {m}^{2} }

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