Question

Find the volume of a cuboid if its surface area is 208 cm2 and the ratio of length, breadth and height
is 2 : 3: 4.​

Answer 1

Answer:

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Answer 2

${ \sf { \huge {\green { \underline {solution}}}}}$

${ \rm{ \large \bold{ \underline{given \colon}}}}$

${ \rm{ \large{the \: curve \: surface \: area = 208{cm}^{2} }}}$

${ \rm{ \large{let \: the —}}}$

${ \rm{ \large{ \bull length = 2x}}}$

${ \rm{ \large{ \bull bredth = 3x}}}$

${ \rm{ \large{ \bull height = 4x}}}$

${ \rm{ \large \bold{ \therefore \: curve \: surface \: area = }}} { \rm{2(lb + bh + hl)}}$

${ \rm{ \large {208 = { \rm{2 \{(2x.3x) + (3x.4x) + (4x.2x) \}}}}}}$

${ \rm{ \large { \implies208 = { \rm{2 \{ {6x}^{2} + {12x}^{2} + {8x}^{2} \}}}}}}$

${ \rm{ \large { \implies208 = { \rm{2 \times {26x}^{2} }}}}}$

${ \rm{ \large { \implies208 = { \rm{ {52x}^{2} }}}}}$

${ \rm{ \large { \implies {52x}^{2} = { \rm{ 208 }}}}}$

${ \rm{ \large { \implies {x}^{2} = { \rm{ \dfrac{208}{52} }}}}}$

${ \rm{ \large { \implies {x}^{2} = { \rm{ 4 }}}}}$

${ \rm{ \large { \implies {x}= { \rm{ 2 }}}}}$

${ \rm{ \large{ \therefore2x = 2 \times 2 = 4}}}$

${ \rm{ \large{ 3x = 3 \times 2 = 6}}}$

${ \rm{ \large{ 4x = 4 \times 2 = 8}}}$

${ \rm{ \large \bold{ \therefore volume = }}} { \rm{l.b.h}}$

${ \rm{ \large { \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 4 \times 6 \times 8}}}$

${ \rm{ \large { volume= 192 {cm}^{3} }}}$