Question

2. What is the volume of a cube (in cm') whose diagonal measures 4√3 cm?
3. The whole surface area of a rectangular block is 8788 cm2. If the length, breadth and height are in the
bo 4: 3:2. find the difference between its length and height.
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Answer 1

Solution ✌️✌️✌️

diagonal(d)=4√3 cm

let the side of the cube is =a

now..

$= > d {}^{2} = a {}^{2} + ( \sqrt{2} a) {}^{2} \\ = > d {}^{2} = a {}^{2} + 2a {}^{2} = 3a {}^{2} \\ = > d = \sqrt{3} a \\ = > a = \frac{d}{ \sqrt{3} } \\ = > a = \frac{4 \sqrt{3} }{ \sqrt{3} } \\ = > a = 4 \: cm$

therefore volume of the cube =4³ cm³=64cm³

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let the length, breadth and height are 4x ,3x and 2x

now ...total surface area of a cuboid is

=2(lb+bh+lh)

=2[(4x)(3x)+(3x)(2x)+(2x)(4x)] cm²

=2(12x²+6x²+8x²)

=2(26x²).

=(52x² ) cm²

now..

52x²=8788

=>x²=8788/52=169

=>X=13

now... length=4(13)=52cm

breadth=3(13)=39cm

height=2(13)=26 cm

difference between length and height is...

=(52-26)cm

=26 cm

•••••Hope this helps u•••••