Question

Please help with question 1

Answer 1

Answer:

The volume of Solid A is 120 cm³.

Step-by-step explanation:

Given the area of the solids are in the ratio: 4 : 9

Let their actual areas be 4x² and 9x². We have assumed the common ratio as x² for easier computation.

We have area: $A_A : A_B =$    4x²       :     9x²

This implies, the length should have been of the ratio of the square root of these numbers.

Therefore, the ratios of the lengths is: $\sqrt{4x^2} : \sqrt{9x^2}$

$L_A : L_B = 2x : 3x$

Now, volume is cube of lengths. Therefore, the ratio of volumes would be:

$V_A : V_B = 8x^3 : 27x^3$

Given $V_B = 405 cm^3$

$\implies 27x^3 = 405 \hspace{1mm} cm^3$

$\implies x^3 = \frac{405}{27} = 15$

Hence, the volume of solid A, $V_A = 8x^3 = 8 \times 15 = \textbf{120} \hspace{1mm} cm^3$.

Hence, the answer.