Question

The breadth and height of a cuboid are 5 cm and 3 cm, respectively. If the volume of the cuboid is 90 cm3, then what is its length? ​

Answer 1

$\sf Given \begin{cases} & \sf{Breadth \; of \; cuboid \; is \; \bf{5\;cm}} \\\ &\sf{Height \; of \; cuboid\; is \; \bf{ 3\;cm}} \\ &\sf{Volume \; of \; cuboid \; is \; \bf{90\;cm^3}} \end{cases}$

Need to find: The length of the cuboid.

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❍ Let the Length of the cuboid be l cm.

$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}$⠀⠀⠀⠀

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$\star\; \boxed{\sf{\pink{Volume_{\;(cuboid)} = l \times b \times h}}}$

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• Here, l is the length of the cuboid, b is the Breadth of the cuboid and h is the height of the cuboid. Volume of the cuboid is given that is 90 cm³.

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Therefore,

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$:\implies\sf Length \times Breadth \times Height = Volume \\\\\\:\implies\sf l \times 5 \times 3 = 90 \\\\\\:\implies\sf l \times 15 = 90 \\\\\\:\implies\sf l = \cancel\dfrac{90}{15} \\\\\\:\implies{\underline{\boxed{\frak{\pink{l = 6}}}}}\;\bigstar$

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$\therefore{\underline{\sf{Hence,\: Length\; of \; cuboid\: is \; \bf{ 6\;cm}.}}}$

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

• $\sf Volume\:of\:cuboid = l \times b \times h$

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

• $\sf Curved\:surface\:area\:of\:cuboid = 2(l + b)h$

• $\sf Diagonal\:of\:cuboid = \sqrt{l^2 + b^2 + h^2}$

Answer 2

Answer:

Length =6cm

Step-by-step explanation:

Length x breadth x height = 90cm^3

length x 5 x 3 = 90cm^3

length = 90/15

length =6cm