Question

find the height of cuboid whose base area is 80 cm square and volume is 900 cm square​

Answer 1

$\sf Given \begin{cases} & \sf{Base\:area_{\:(cuboid)} = \bf{80\:cm^2}} \\ & \sf{Volume_{\:(cuboid)} = \bf{900\:cm^3}} \end{cases}$

To find: Height of cuboid?

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☯ Let Length, breadth & height of cuboid be l, b & h respectively.

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$\setlength{\unitlength}{0.74 cm}\begin{picture}(0,0)\thicklines\put(3.5,6.1){\sf b\:cm}\put(7.7,6.3){\sf l\:cm}\put(11.3,7.45){\sf h\:cm}\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\put(4,7.3){\line(1,0){5}}\put(4,10.3){\line(1,0){5}}\put(9,10.3){\line(0,-1){3}}\put(4,7.3){\line(0,1){3}}\put(6,6){\line(-3,2){2}}\put(6,9){\line(-3,2){2}}\put(11,9){\line(-3,2){2}}\put(11,6){\line(-3,2){2}}\end{picture}$

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$\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}$

Base Area of cuboid = 80 cm².

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$:\implies\sf Base\:Area = Length \times breadth\\ \\ \\ :\implies\sf l \times b = 80\qquad\qquad\bigg\lgroup\bf eq\:(1) \bigg\rgroup$

And,

Volume of cuboid = 900 cm³

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$\dag\;{\underline{\frak{As\;we\;know\;that,}}}$

$\star\;{\boxed{\sf{\pink{Area_{\;(cuboid)} = length \times breadth \times breadth}}}}$

$\qquad\qquad:\implies\sf l \times b \times h = 900$

$:\implies\sf 80 \times h = 900\qquad\qquad\bigg\lgroup\bf From\:eq\:(1) \bigg\rgroup$

$\quad:\implies\sf h = \cancel{\dfrac{900}{80}}\\ \\ \\ :\implies{\underline{\boxed{\frak{\purple{h = 11.25\:cm}}}}}\;\bigstar$

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$\qquad\boxed{\bf{\mid{\overline{\underline{\pink{\bigstar\: Formulas\:related\:to\:cuboid:}}}}}\mid}$

$\sf Base\: Area\: of\: cuboid = \bf{l \times b}$

$\sf Total\:surface\:area\:of\: cuboid = \bf{2(lb + bh + hl)}$

$\sf Curved\:surface\:area\:of\: cuboid = \bf{2(l + b) \times h}$

$\sf Volume\:of\:cuboid = \bf{l \times b \times h}$

Answer 2

Answer:

$height \: o \: cuboid = \frac{volume}{base \: area} \\ \\ \\ = \frac{900 \: {cm}^{3} }{80 \: {cm}^{2} } \\ \\ \\ = 11.25 \: cm$