Mensuration Practice Test 11

Let radius of A = r
And radius of B = R
If Surface area of A = 1
Then surface area of B = 4 [∵ it is 300% higher]
$\frac{4\mathit{\pi }{\mathit{r}}^2}{4\mathit{\pi }{\mathit{R}}^2}$ = $\frac{1}{4}$
$\frac{\mathit{r}}{\mathit{R}}$ = $\sqrt{\frac{1}{4}}$
$\frac{\mathit{r}}{\mathit{R}}$ = $\frac{1}{2}$
So, if r = 1
Then R = 2
$\frac{\mathrm{Volume}\mathrm{of}\mathrm{A}}{\mathrm{Volume}\mathrm{of}\mathrm{B}}$ = $\frac{\frac{4}{3}\mathit{\pi }{\mathit{r}}^3}{\frac{4}{3}\mathit{\pi }{\mathit{R}}^3}$ = $\frac{{\left(1\right)}^3}{{\left(2\right)}^3}$ = $\frac{1}{8}$
So, if volume of A = 1
Then volume of B = 8
Volume of B is $\frac{7}{8}$ times more than the volume of A
$\frac{7}{8}\times 100$ = 87.5 times