Question

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Answer 1

Answer:

3. (15x^4y)+(5* x^2* y^2)/8

Step-by-step explanation:

Given values are length and breadth, so area of rectangle is l*b

= (3 * x^2* y + y^2) *(5 * x^2)/8

Answer 2

Formulae Used :

$\sf \bullet \: \: Volume \: of \: cuboid \: = \: length \: \times \: breadth \: \times \: height \\ \\ \sf \bullet \: Area \: of \: rectangle \: = \: length \: \times Breadth \: \\ \\ \sf \bullet \: {a}^{m} \times {a}^{n} = \: {a}^{(m + n)}$

SOLUTION :

(2) Volume of box -

Given - Dimensions of box

• 3xy²
• (1/7)x³
• (4/5)x²y

$\sf \implies \: Volume \: of \: box \: = \: 3x {y}^{2} \times \dfrac{1}{7} {x}^{3} \times \frac{4}{5} {x}^{2} y \\ \\ \sf \implies \: Volume \: of \: box \: = \: \dfrac{(3 \times 4)}{(7 \times 5)} \: \bigg( {x}^{(1 + 3 + 2)} \bigg) \times \bigg( \: {y}^{(2 + 1)} \: \bigg) \\ \\ \sf \implies \: Volume \: of \: box \: = \: \dfrac{12}{35} {x}^{6} {y}^{3}$

(3) Area of rectangle -

Given - Dimension of rectangle

• Length = 3x²y + y²
• Breadth = (5/8)x²

$\sf \implies \: Area \: of \: rectangle \:=\: \bigg(\: 3x^2y\:+\:y^2\:\bigg) \times \bigg( \dfrac{5}{8}x^2\: \bigg) \\ \\ \sf \implies \: Area \: of \: rectangle \:=\: \bigg( \: 3x^2y\: \times \dfrac{5}{8}x^2\: \: \bigg) \: + \: \bigg( \: {y}^{2} \times \dfrac{5}{8}x^2\: \bigg) \\ \\ \sf \implies \: Area \: of \: rectangle \:=\: \dfrac{(3 \times 5)}{8} \bigg( {x}^{(2 + 2)} y \bigg) \: + \: \bigg( \: \dfrac{5}{8} {x}^{2} {y}^{2} \bigg) \\ \\ \sf \implies \: Area \: of \: rectangle \:=\: \dfrac{15}{8} {x}^{4} y \: + \: \dfrac{5}{8} {x}^{2} {y}^{2}$