Question

the ratio of total surface area of a solid hemisphere and the surface area of a sphere is 27: 64. find the ratio of their raddi​

Answer 1

Step-by-step explanation:

Let the radii of hemisphere and sphere be R and r respectively.

$\frac{TSA \: of \: hemisphere}{SA \: of \: sphere} = \frac{27}{64} \\ \\ \therefore \: \frac{3\pi \: {R}^{2} }{4\pi \: {r}^{2}} = \frac{27}{64}\\ \\ \therefore \: \frac{3 \: {R}^{2} }{4 {r}^{2}} = \frac{27}{64} \\ \\ \therefore \: \frac{{R}^{2} }{{r}^{2}} = \frac{27}{64} \times \frac{4}{3} \\ \\ \therefore \: \frac{{R}^{2} }{{r}^{2}} = \frac{9}{16} \\ \\ \therefore \: \frac{{R}}{{r}} = \sqrt{ \frac{9}{16} } \\ \\ \therefore \: \frac{{R}}{{r}} = \frac{3}{4} \\ \\ \huge \purple{ \boxed{\therefore \: R : \: r = 3 \: : \: 4}}$