Question

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Q1.The length breadth and height of a cuboid are in the ratio 5:3:2, and its total area is 3968 cm2. Find the dimensions of the cuboid.​

Answer 1

Answer:

length=64cm×5=320cm

breadth =64cm×3=192cm

height =64cm×2=128cm

Explanation:

let the length =5x

breadth=3x

and height=2x

then surface area of cuboid =2(lb+bh+lh) sq units

so ATQ

2(lb+bh+lh) sq units=3968CM²

=2(5x×3x+2x×3x+2x×5x)cm²=3968cm²

2(15x+6x+10x)cm²=3968cm²

2(31x)cm²=3968

cm²

62xcm²=3968cm²

x=

$\frac{3968 {cm}^{2} }{62 {cm}^{2} } = 64 cm$

so length=64cm×5=320cm

breadth =64cm×3=192cm

height =64cm×2=128cm

Answer 2

Given :

Height of Cylinder is 14 cm .

C.S.A of Cylinder is 88 cm² .

To Find :

Diameter of the base .

Solution :

$\longmapsto\tt{Height=14\:cm}$

Using Formula :

$\longmapsto\tt\boxed{C.S.A\:of\:Cylinder=2\:pi{rh}}$

Putting Values :

$\longmapsto\tt{88=2\times\dfrac{22}{{\cancel{7}}}\times{r}\times{{\cancel{14}}}}$

$\longmapsto\tt{88=44\times{2}\times{r}}$

$\longmapsto\tt{88=88r}$

$\longmapsto\tt{r=\cancel\dfrac{88}{88}}$

$\longmapsto\tt\bf{r=1\:cm}$

As we know that Diameter is double of Radius . So ,

$\longmapsto\tt{Diamtere=2r}$

$\longmapsto\tt{2(1)}$

$\longmapsto\tt\bf{2\:cm}$

So , The Diameter of the base of Cylinder is 2 cm .