Question

find the volume of the cuboids whose dimensions are (x+3),(x+5) and (x+2)​

Answer 1

$\large \mathfrak \purple {☞~~Question:-}$

Find the volume of the cuboids whose dimensions are (x + 3), (x + 5) and (x + 2).

$\large \mathfrak \purple {☞~~Solution:-}$

Given,

• Length = (x + 3) units
• Breadth = (x + 5) units
• Height = (x + 2) units

$\boxed {\bf\red {Volume~of~a~cuboid=(Length )(Breadth)(Height)} }$

$\blue {:\implies} \sf (x + 3)(x + 5)(x + 2) \: units^3$

$\blue {:\implies}\sf ({x}^{2} + 5x + 3x + 15)(x + 2)$

$\blue {:\implies} \sf ( {x}^{2} + 8x + 15)(x + 2)$

$\blue {:\implies}\sf x^3 + 2 x^2 + 8 x^2 + 16x + 15x + 30$

$\blue {:\implies}\sf {x}^{3} + 10 {x}^{2} + 31x + 30 \: {units}^{3}$

$\boxed {\bf \red {\therefore~Volume~of~the~cuboid=x^3+10x^2+31x+30~units^3}}$

$\large \mathfrak \purple {☞~~Know~more:-}$

• Volume of cube = $\sf a^3$
• Volume of cylinder = $\sf \pi r^2h$
• Volume of sphere = $\sf \cfrac{4}{3} \pi r^3$

_____________________

$\boxed {\red {\longmapsto \bf Sita05}}$

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Answer 2

Given

• Dimensions of cuboid :
• Length = (x + 3) units
• Breadth = (x + 5) units
• Height = (x + 2) units

To find

• Volume of cuboid

Solution

Volume of cuboid = Length × Breadth × Height

• (x + 3) (x + 5) (x + 2)
• (x)(x) + (x)(5) + 3(x) + 3(5) (x + 2)
• (x² + 5x + 3x + 15) (x + 2)
• (x² + 8x + 15) (x + 2)
• (x²)(x) + (8x)(x) + (15)(x) + (x²)(2) + (8x)(2) + (15)(2)
• x³ + 8x² + 15x + 2x² + 16x + 30
• x³ + 10x² + 31x + 30

Hence, the volume of cuboid is x³ + 10x² + 31x + 30 unit³