Question

a solid is hemispherical at the bottom and conical (of same radius) above it. If the surface areas of the two parts are equal, then the ratio of its radius and the slant height of the conical part is _______​

Answer 1

$\huge\underline\blue{\sf Given:}$ It has been said that they have same surface Area ...

Question:- we have to Find ratio of radius and slant Height . ( since its very easy what you asked),( i think you want to know ratio of Radius and Height of cone )

My Approach :----

we know that surface area of Hemisphere = 2πr²

Surface area of cone = πrl

A/q,

$2\pi \: r^{2} = \pi \: r \: l \\ \\ 2r = l \\ \\ \\ and \: we \: know \: that \: \\ height \: of \: cone \: = \sqrt{(l ^{2} - r ^{2} ) } \\ \\ so \\ \\ h = \sqrt{4 {r}^{2} - {r}^{2} } \\ \\ h = r \sqrt{3} \\ \\ so$

r:h = r : r√3

$\large\red{\boxed{\sf </u></strong><strong><u>r</u></strong><strong><u>:</u></strong><strong><u>h\</u></strong><strong><u>:</u></strong><strong><u>=</u></strong><strong><u>\</u></strong><strong><u>:</u></strong><strong><u>1</u></strong><strong><u>:</u></strong><strong><u>\sqrt{3}</u></strong><strong><u>}}$

Answer 2

Answer:

r:l=1:2

Step-by-step explanation: