Question

NEED QUICK
The volumes of two similar solids are 1331 m3 and 343 m3. The surface area of the larger one is 484 m2. What is the surface area of the smaller one?

1372 m2

196 m2

343 m2

none of these

Answer 1

none of them i belive

Answer 2

To solve this question we will have to make note of an important fact of geometry. That is, "volume is proportional to the cubed of the linear dimensions and that surface area is proportional to the squared of the linear dimensions".

Now, let the volume of the larger solid be $V_1$ and the volume of the smaller solid be $V_2$

Let the linear dimension of the larger solid be $L_1$ and the linear dimension of the smaller solid be $L_2$.

Now, it has been given in the question that, $V_1 =1331 m^3$ and $V_2=343 m^3$. Therefore the ratio is:

$\frac{V_1}{V_2}=\frac{1331}{343}$.............(Equation 1)

Therefore, the cuberoot of the above equation will give us the ratio of the linear dimensions as:

$\frac{L_1}{L_2}=\sqrt[3]{\frac{1331}{343}}=\frac{11}{7}$...(Equation 2)

Let $S_1$ be the surface area of the larger solid. Then, we know that, $S_1=484 m^2$. Let $S_2$ be the surface area of the smaller solid. Then we know that, the ratio of the surface area will be the squared of the linear dimensions. Thus, the squared of the ratio of the linear dimensions in (Equation 2) will be equal to the ratio of the surface areas.

Thus, we will have:

$\frac{S_1}{S_2}=(\frac{L_1}{L_2} )^2=(\frac{11}{7})^2=\frac{121}{49}$

$\because S_1= 484 m^2$ (given), we can easily find $S_2$ as:

$\frac{484}{S_2}= \frac{121}{49}$

Thus, $S_2=\frac{484\times 49}{121}=196 m^2$

Therefore, from the given options, the second option is the correct answer.