Question

Find the height of a Cuboid whose volume is 275 cm³ and base area is 25 cm².​

Answer 1

Given:-

• Volume of a Cuboid is 275 cm³.
• Base area of a Cuboid is 25 cm².

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To find:-

• Height of a Cuboid.

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Solution:-

Here,

• Base (b) = 25 cm²
• Volume = 275 cm³

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☆Formula used:-

${\dag}\:{\underline{\boxed{\sf{\purple{Volume_{(Cuboid)} = base \times height}}}}}$

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$\tt\longmapsto{275 = 25 \times h}$

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$\tt\longmapsto{h = \dfrac{275}{25}}$

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$\sf\longmapsto{\boxed{\red{h = 11\: cm}}}$

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Hence,

• the height of the Cuboid is 11 cm.

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★More to know :-

$\sf{Area\;of\;Rectangle\;=\;Length\;\times\;Breadth}$

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$\sf{Area\;of\;Square\;=\;(Side)^{2}}$

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$\sf{Area\;of\;Triangle\;=\;\dfrac{1}{2}\;\times\;Base\;\times\;Height}$

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$\sf{Area\;of\;Parallelogram\;=\;Base\;\times\;Height}$

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$\sf{Area\;of\;Circle\;=\;\pi r^{2}}$

$\sf{Perimeter\;of\;Rectangle\;=\;2\;\times\;(Length\;+\;Breadth)}$

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$\sf{Perimeter\;of\; Square\;=\;4\;\times\;(Side)}$

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$\sf{Perimeter\;of\;Circle\;=\;2\pi r}$

Answer 2

AnswEr -:

• $\underline{\boxed{\star{\sf{\blue{ Height_{(Cuboid)} \: = \: 11cm }}}}}$

Explanation,

Given ,

• The base of cuboid is 25 cm² .
• Volume of Cuboid is 275 cm ³

☆ Figure of Cuboid-:

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

To Find,

• The height of Cuboid .

Now ,

• $\underline{\boxed{\star{\sf{\purple{Volume_{Cuboid}\:: Base \times Height }}}}}$

Here ,

• Base of Cuboid-: 25 cm²
• Volume of Cuboid-: 275 cm ²

Now,

• $\implies{\sf{\large {275 cm³ = 25 \times Height }}}$
• $\implies{\sf{\large {\frac {275}{25} = Height }}}$
• $\implies{\sf{\large { Height \: = \: 11 cm }}}$

Hence,

$\underline{\boxed{\star{\sf{\blue{ Height_{(Cuboid)} \: = \: 11cm }}}}}$

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☆ Formulas related to Cuboid-:

• Total Surface area = 2 (Length x Breadth + breadth x height + Length x height)
• Lateral Surface area = 2 height(length + breadth)
• Volume of the cuboid = (length × breadth × height)
• Diagonal of the cuboid =√( length ² + breadth ² + height²)
• Perimeter of cuboid = 4 (length + breadth + height)

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