Question 16
What are the possible expressions for the dimensions of the cuboids whose volumes are given below?
$\begin{matrix} \begin{matrix} V o l u m e : 3 x^{2} - 12 x \end{matrix} (i) \end{matrix} \begin{matrix} \begin{matrix} V o l u m e : 12 k y^{2} + 8 k y - 20 k \end{matrix} (i i) \end{matrix}$

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Solution

$(i) V o l u m e o f c u b o i d = a b c = 3 x^{2} - 12 x = 3 x (x - 4)$

$∴ 3, x(x-4) are the three factors.$
So, these can be the three dimensions.

$(i i) V o l u m e o f c u b o i d = a b c = 12 k y^{2} + 8 k y - 20 k = 4 k (3 y^{2} + 2 y - 5) = 4 k [3 y (y - 1) + 5 (y - 1)] = 4 k (y - 1) (3 y + 5)$

$∴ 4k, (y-1) and (3y+5) are the three factors.$
Hence, these can be the three dimensions.

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Similar questions

What are the possible expressions for the dimensions of the cuboid whose volumes are given below?
(i) Volume: ${3 x}^{2} - 12 x$

(ii) Volume: $12 k y^{2} + 8 k y - 20 k$

12 k y^{2} + 8 k y - 20 k

V o l u m e : 12 k y^{2} + 8 k y - 20 k

What are the possible expressions for the dimensions of cuboid , whose volume is : 12ky^2 +8ky- 20 k?

3 x^{2} - 12 x

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