Question

please solve my question with step by step​

Answer 1

HERE

let r is the radius, h is the height and l is the slant height of the smaller cone respectively.

Now in ΔOAB and ΔOCD,

∠OAB = ∠OCD {each 90}

∠AOB = ∠COD {common}

So, by AA similarity,

ΔOAB ≅ ΔOCD

=> OB/OD = AB/CD = OA/OC

=> l/L = r/R = h/H

Now, curved surface area of the smaller cone = curved surface area of the cone - curved surface area of the frustum

=> curved surface area of the smaller cone = (1 - 8/9) * curved surface area of the cone

=> curved surface area of the smaller cone = (1/9) * curved surface area of the cone

=> curved surface area of the smaller cone/curved surface area of the cone = 1/9

=> πrl/πRL = 1/9

=> rl/RL = 1/9

=> (r/R)*(l/L) = 1/9

=> (h/H)*(h/H) = 1/9 {using equation 1}

=> (h/H)2 = 1/9

=> (h/H) = 1/3

=> h = H/3

Now, OA/AC = h/(h - h)

=> OA/AC = (H/3)/(H - H/3)

=> OA/AC = (H/3)/(2H/3)

=> OA/AC = 1/2

=> OA : AC = 1 : 2

Answer 2

$\normalsize\;\;\bullet\;\sf Perimeter\;of\;square\;\; \red{4\times side} \\\\ \normalsize\;\;\bullet\;\sf Perimeter\;of\;Rectangle\;\; \purple{ 2(l + b)} \\\\ \normalsize\;\;\bullet\;\sf Area\;of\;Square\;\; \blue{side \times side} \\\\ \normalsize\;\;\bullet\;\sf Area\;of\;Rectangle\;\; \green{ length \times breadth} \\\\ \normalsize\;\;\bullet\;\sf Area\;of\;triangle\;:\; \red{\dfrac{1}{2} \times\:base\:\times height}$

$\normalsize\;\;\bullet\;\sf Perimeter\;of\;square\;\; \red{4\times side}$

tex]\normalsize\;\;\bullet\;\sf Perimeter\;of\;square\;\; \red{4\times side} \\\\ \normalsize\;\;\bullet\;\sf Perimeter\;of\;Rectangle\;\; \purple{ 2(l + b)} \\\\ \normalsize\;\;\bullet\;\sf Area\;of\;Square\;:\; \blue{side \times side}[/tex]

$\normalsize\;\;\bullet\;\sf Perimeter\;of\;square\;\; \red{4\times side} \\\\ \normalsize\;\;\bullet\;\sf Perimeter\;of\;Rectangle\;\; \purple{ 2(l + b)}$

$\normalsize\;\;\bullet\;\sf Area\;of\;Square\;:\; \blue{side \times side}$

$\normalsize\;\;\bullet\;\sf Perimeter\;of\;square\;\; \red{4\times side} \\\\ \normalsize\;\;\bullet\;\sf Perimeter\;of\;Rectangle\;\; \purple{ 2(l + b)} \\\\ \normalsize\;\;\bullet\;\sf Area\;of\;Square\;\; \blue{side \times side} \\\\ \normalsize\;\;\bullet\;\sf Area\;of\Rectangle\;\; \green{ length \times breadth}$

$\normalsize\;\;\bullet\;\sf Area\;of\;Rectangle\;\; \green{ length \times breadth}$

$\normalsize\;\;\bullet\;\sf Area\;of\;triangle\;:\; \red{\dfrac{1}{2} \times\:base\:\times height}$