Question

The volume of the cuboid is 3584 cm?. Its base is a square and height is 14 cm, find
(i) the side of the square base
(ii) surface area of the cuboid.
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Answer 1

$\\ \large\underline{ \underline{ \sf{ \red{given:} }}}$

• Volume of cuboid is 3584cm³.

• Base of the cuboid is square.

• Height is 14cm.

$\\ \\ \large\underline{ \underline{ \sf{ \red{to \: find:} }}}$

• Side of the square base.

• Surface area of cuboid.

$\\ \\ \large\underline{ \underline{ \sf{ \red{solution:} }}}$

$\\ \huge \boxed{ \bf \: (i)}$

Let the side of square base be "x".

$\\ \star \small\boxed{\sf \: volume\: of \: cuboid =area \: of \: base \times height }$

Base is square ( given )

⋆ Area of base = x²

➣ Putting value we get...

➙ 3584 = x² × 14

➙ x² = 3584/14

➙ x² = 256

➙ x = 16cm

Hence , side of square base is 16cm.

$\\ \\ \huge \boxed{ \bf \: (ii)}$

Sides of the cuboid are 16cm , 16cm , 14cm.

• Length = 16cm.

• Breadth = 16cm.

• Height = 14cm.

$\\ \boxed{ \sf \: area \: of \: cuboid = 2(lh + bh + lb)}$

➣ Putting values , we get..

➙ Area = 2 [ 16(14) + 16(14) + 16(16) ]

➙ Area = 2 [ 224 + 224 + 256 ]

➙ Area = 2 [ 704 ]

➙ Area = 1408cm²

Hence , Area of cuboid is 1408cm².

Answer 2

Answer is in attatchment

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