Question

The volume of a cuboid is 1536 mº. Its length is 16 m, and its breadth
and height are in the ratio 3:2. Find the breadth and height of
the cuboid.​

Answer 1

Answer:

1536m³=16(3x)(2x)

1536=96x²

16=x²

x=4m

Breadth=3×4=12m

Height=2×4=8m

Hope it helps you.

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Answer 2

Given:

• Volume of cuboid is 1536 m³.
• Length of cuboid = 16 m
• Ratio of breadth and height of cuboid is 3:2.

⠀⠀⠀⠀

To find:

• Breadth and Height of cuboid?

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━

☯ Let the breadth and height of cuboid be 3x and 2x respectively.

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$\setlength{\unitlength}{0.68cm}\begin{picture}(12,4)\linethickness{0.3mm}\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\put(4,7.3){\line(1,0){5}}\put(4,10.3){\line(1,0){5}}\put(9,10.3){\line(0,-1){3}}\put(4,7.3){\line(0,1){3}}\qbezier(6,6)(4,7.3)(4,7.3)\qbezier(6,9)(4,10.2)(4,10.3)\qbezier(11,9)(9.5,10)(9,10.3)\qbezier(11,6)(10,6.6)(9,7.3)\put(8,5.5){\sf{16 m}}\put(4,6){\sf{3x}}\put(11.5,7.5){\sf{2x}}\end{picture}$

⠀⠀⠀⠀

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

$\star\;{\boxed{\sf{\purple{Volume_{\;(cuboid)} = length \times breadth \times height}}}}$

$:\implies\sf 16 \times 3x \times 2x = 1536$

$:\implies\sf 16 \times 6x^2 = 1536$

$:\implies\sf 6x^2 = \cancel{ \dfrac{1536}{16}}$

$:\implies\sf 6x^2 = 96$

$:\implies\sf x^2 = \cancel{ \dfrac{96}{6}}$

$:\implies\sf x^2 = 16$

$:\implies\sf \sqrt{x^2} = \sqrt{16}$

$:\implies{\underline{\boxed{\frak{\pink{x = 4}}}}}\;\bigstar$

Therefore,

⠀⠀⠀⠀

• Breadth of cuboid, 3x = 3 × 4 = 12 m
• Height of cuboid, 2x = 2 × 4 = 8 m

⠀⠀⠀⠀

$\therefore\;{\underline{\sf{Hence,\;the\;breadth\;and\; height\;of\;cuboid\;is\; {\textsf{\textbf{12\;m\;and\;8\;m}}}.}}}$

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━

$\quad\qquad\qquad\boxed{\bf{\mid{\overline{\underline{\pink{\bigstar\: More\:to\:know}}}}}\mid}$

$\begin{array}{|c|c|c|}\cline{1-3}\bf Shape&\bf Volume\ formula&\bf Surface\ area\ formula\\\cline{1-3}\sf Cube&\tt l^3}&\tt 6l^2\\\cline{1-3}\sf Cuboid&\tt lbh&\tt 2(lb+bh+lh)\\\cline{1-3}\sf Cylinder&\tt {\pi}r^2h&\tt 2\pi{r}(r+h)\\\cline{1-3}\sf Hollow\ cylinder&\tt \pi{h}(R^2-r^2)&\tt 2\pi{rh}+2\pi{Rh}+2\pi(R^2-r^2)\\\cline{1-3}\sf Cone&\tt 1/3\ \pi{r^2}h&\tt \pi{r}(r+s)\\\cline{1-3}\sf Sphere&\tt 4/3\ \pi{r}^3&\tt 4\pi{r}^2\\\cline{1-3}\sf Hemisphere&\tt 2/3\ \pi{r^3}&\tt 3\pi{r}^2\\\cline{1-3}\end{array}$