Question

please answer my question​

Answer 1

Answer:

Let the side of the three identical cubes be 'a'.

If they are joined to form a cuboid, then:

length=3a, breadth=a, height=a

To Find: Ratio of (TSA of resulting Cuboid) to (Sum of TSA of 3 cubes)

Sol.ⁿ:

TSA of one cube with side 'a'=6a²

So, sum TSAs of 3 cubes=18a² [∵6a²×3]

Now, as;

TSA of a cuboid=2(lb+bh+lh)

So,

TSA of resulting cuboid formed:

=2[(3a)(a)+(a)(a)+(3a)(a)]

=2[3a²+a²+3a²]

=2×7a²

=14a²

Now, Ratio:

$= \frac{14 {a}^{2} }{18 {a}^{2} }$

$= \frac{7}{9}$

So, the Ratio of the Total surface area of the cuboid to sum of that of the smaller cubes is equal to '7:9'

Answer 2

ANSWER

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$let \: the \: edge \: of \: cube \: be \: x unit \: \\ \\ total \: surface \: area \: of \: cube = 6 {l}^{2} \\ = 6 {x}^{2} unit {}^{2} \\total \: surface \: area \: of \: 3 \: such \: cubes = 3 \times 6 {x}^{2} unit \\ = 18 {x}^{2} unit {}^{2} \\ \\ when \: three \: such \: cubes \: are \: placed \: adjacent \: to \: each \: \\ other \: then \\ length = 3x \: unit \\ breadth = x \: unit \\ height = x \: unit \\ \\ total \: surface \: of \: new \: cuboid \: = 2(lb + bh + lh) \\ = 2(3x \times x + x \times x + x \times 3x) \\ = 2(3 {x}^{2} + {x}^{2} + 3 {x}^{2} ) \\ = 2(7 {x}^{2} ) \\ = 14 {x}^{2} unit {}^{2} \\ \\ ratio = \frac{18 {x}^{2} }{14 {x}^{2} } = \frac{9}{7} \\ \\ hence \: the \: ratio \: is \: 9 \: is \: to \: 7$

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