Question

the dimensions of a cuboid are in the ratio 5 :3: 2 its volume is 21870 cm³ find its total surface area.​

Answer 1

$\large\underline{ \underline{ \sf \maltese{ \: Question:- }}}$

The dimensions of a cuboid are in the ratio 5 :3: 2 its volume is 21870 cm³ find its total surface area.

$\large\underline{ \underline{ \sf \maltese\green{ \: Given:- }}}$

• Length = 5x
• Breadth = 3x
• Height = 2x
• Volume = 21870cm³

$\large\underline{ \underline{ \sf \maltese\green{ \: </strong><strong>Solution</strong><strong>:- }}}$

$\begin{gathered}\begin{gathered}\begin{gathered}: \implies \underline\blue{ \boxed{\displaystyle \sf \bold\orange{\: Volume\: of \: Cuboid \: = \: Length \: \times \: Breadth\: \times \: Height }} }\\ \\\end{gathered}\end{gathered}\end{gathered}$

$\qquad \quad {:} \longrightarrow \sf{\sf{21870 \: = \: \red{5x} \: \times \red{3x} \: \times \red{2x} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{21870 \: = \: 30{x}^{3} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ \cancel \blue{\frac{21870}{30}} \: = \: {x}^{3} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ 729 \: = \: {x}^{3} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ \sqrt[3]{729} \: = \: {x} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ \red{3 \times 3 \times 3}\: \: \times \green{3 \times 3 \times 3 } \: = \: {x} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ 3 \: \times \: 3\: = \: {x} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ 9 \: = \: {x} }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{x \: = \: 9 }}}$

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$\underbrace\orange{\boxed{ \sf \purple{ Measures \: of \: Dimensions }}}$

• Length = 5x = 5 × 9 = 45cm
• Breadth = 3x = 3 × 9 = 27cm
• Height = 2x = 2 × 9 = 18cm

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$\begin{gathered}\begin{gathered}\begin{gathered}: \implies \underline\blue{ \boxed{\displaystyle \sf \bold\orange{\: Total\: Surface\: Area\: = \: 2(lb \: + \:bh \: + \: lh) }} }\\ \\\end{gathered}\end{gathered}\end{gathered}$

$\qquad \quad {:} \longrightarrow \sf{\sf{T.S.A \: = \: 2(45 \times 27 \: + \: 27 \times 18 \: + \: 45 \times 18) }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{T.S.A \: = \:2(1215 \: + \: 486 \: + \: 810) }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{T.S.A \: = \:2\: \times \: 2511 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{T.S.A \: = \: 5022 }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{Total \: Surface \: Area \: = \: 5022sq.cm}}}$

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$\underbrace\orange{\boxed{ \sf \red{ Diagram}}}$

$\setlength{\unitlength}{0.74 cm}\begin{picture}\thicklines\put(5.6,5.4){\bf A}\put(11.1,5.4){\bf B}\put(11.2,9){\bf C}\put(5.3,8.6){\bf D}\put(3.3,10.2){\bf E}\put(3.3,7){\bf F}\put(9.25,10.35){\bf H}\put(9.35,7.35){\bf G}\put(3.5,6.1){\sf 45\:cm}\put(7.7,6.3){\sf 27\:cm}\put(11.3,7.45){\sf 18\:cm}\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\put(4,7.3){\line(1,0){5}}\put(4,10.3){\line(1,0){5}}\put(9,10.3){\line(0,-1){3}}\put(4,7.3){\line(0,1){3}}\put(6,6){\line(-3,2){2}}\put(6,9){\line(-3,2){2}}\put(11,9){\line(-3,2){2}}\put(11,6){\line(-3,2){2}}\end{picture}$

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Answer 2

Answer:

volume of cuboid = l * b * h

= 5x * 3x * 2x = 30x^3

30x^3 = 21870

x = 9

l=5*9 b=3*9 h=2*9

area of cuboid = 2(45*27+45*18+27*18)

=5022 cm square

Step-by-step explanation: