Question

If the area of three adjacent faces of a cuboidal block are in ratio 2:3:4 and its volume is 9,000 cm find its dimensions

Answer 1

$\underline{\sf\: DIAGRAM}$

$\setlength{\unitlength}{0.74 cm}\begin{picture}(12,4)\thicklines\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\put(4,7.3){\line(1,0){5}}\put(4,10.3){\line(1,0){5}}\put(9,10.3){\line(0,-1){3}}\put(4,7.3){\line(0,1){3}}\put(6,6){\line(-3,2){2}}\put(6,9){\line(-3,2){2}}\put(11,9){\line(-3,2){2}}\put(11,6){\line(-3,2){2}}\put(8,5.5){l}\put(4,6.3){b}\put(11.2,7.5){h}\end{picture}$

$\sf\: GIVEN$

• Three adjacent faces of a cuboidal block are in ratio 2:3:4.
• Volume of cuboid is $\sf\:9000{cm}^{3}$.

$\sf\: TO\:FIND$ =It's dimensions.

$\sf\: LET$

• lb = 2x
• bh = 3x
• hl = 4x

$\boxed{\sf\: {(l \times b \times h)}^{3}={Volume}^{2}}$

$\longrightarrow \sf\: 24{x}^{3}= 9000\times 9000 \\ \\ \longrightarrow \sf\: {x}^{3}= \frac{9000 \times 9000}{24} \\ \\ \longrightarrow \sf\: {x}^{3} = \frac{\cancel{9000} \times 9000}{\cancel{24}}\\ \\ \longrightarrow \sf\:{x}^{3}= 375 \times 9000 \\ \\ \longrightarrow \sf\: x = 150 \\ \\ \sf\:So, \\ \\ \longrightarrow \sf\:lb= 2 \times x = 2 \times 150 = 300\\ \\ \longrightarrow \sf\:bh=3 \times x = 3 \times 150 = 450\\ \\ \longrightarrow \sf\:hl=4 \times x = 4 \times 150 = 600\\ \\ \longrightarrow \sf\: l \times b \times h = 9000\\ \\ \implies \sf\: h = \frac{\cancel{9000}}{\cancel{300}}=30\\ \\ \implies \sf\: l = \frac{\cancel{9000}}{\cancel{450}}=20\\ \\ \implies \sf\: b = \frac{\cancel{9000}}{\cancel{600}}=15$

$\boxed{\sf\: Dimension\:of\:cuboid = 20 \times 15 \times 30}$

Answer 2

Answer:

20 15 30 is the right answer