Question

please solve with full explanation​

Answer 1

Given :

• Slant height of cone = 50 cm.
• Radius of cone = 14 cm.

To find :

• Curved surface area of cone.
• Total surface area of cone.
• Volume of cone.

Solution :

Slant height of cone = 50 cm.

Radius of cone = 14 cm.

✪Now find the height of cone✪

We know,

${\boxed{\red{\bold{l^2=h^2+r^2}}}}$

Here ,

• l = Slant height
• r = Radius
• h = height

$\sf{l^2=h^2+r^2}$

$\implies\sf{50^2=h^2+14^2}$

$\implies\sf{2500=h^2+196}$

$\implies\sf{2500-196=h^2}$

$\implies\sf{2304=h^2}$

$\implies\sf{\sqrt{2304}=h}$

$\implies\sf{48=h}$

${\boxed{\sf{Height\:of\:cone=48\:cm}}}$

✪ Now find the curved surface area of the cone ✪

We know,

${\boxed{\bold{\purple{CSA\:of\:cone=\pi\:rl}}}}$

$\sf{\:\:\:\:\:CSA\:of\:cone=\pi\:rl}$

$\implies\sf{CSA\:of\:cone=\frac{22}{7}\times\:14\times\:50\:cm^2}$

$\implies\sf{CSA\:of\:cone=22\times\:2\times\:50\:cm^2}$

$\implies\sf{CSA\:of\:cone=2200\:cm^2}$

${\boxed{\sf{CSA\:of\:cone=2200\:cm^2}}}$

_______________________

✪Now find the total surface area of cone✪

We know,

${\boxed{\bold{\green{TSA\:of\:cone=\pi\:r(r+l)}}}}$

$\sf{\:\:\:\:\:TSA\:of\:cone=\pi\:r(r+l)}$

$\implies\sf{TSA\:of\:cone=\frac{22}{7}\times\:14(14+50)\:cm^2}$

$\implies\sf{TSA\:of\:cone=44\times\:64\:cm^2}$

$\implies\sf{TSA\:of\:cone=2816\:cm^2}$

${\boxed{\sf{TSA\:of\:cone=2816\:cm^2}}}$

_______________________

✪Now find the volume of the cone✪

We know,

${\boxed{\bold{\blue{Volume\:of\:cone=\frac{1}{3}\pi\:r^2h}}}}$

$\sf{\:\:\:\:\: Volume\:of\:cone=\frac{1}{3}\pi\:r^2h}$

$\implies\sf{Volume\: of\:cone=\frac{1}{3}\times\frac{22}{7}\times\:14^2\times\:48\:cm^3}$

$\implies\sf{Volume\: of\: cone=22\times\:2\times\:14\times\:16\:cm^3}$

$\implies\sf{Volume\: of\: cone=9856\:cm^3}$

${\boxed{\sf{TSA\:of\:cone=9856\:cm^3}}}$

_______________________

Answer 2

$\huge{\underline{\red{\rm{Solution:}}}}$

$\large{\underline{\green{\rm{Given:}}}}$

• The slant height of cone=50m
• The radius of cone=14

$\large{\underline{\purple{\rm{To\: Find:}}}}$

• $\sf{C.S.A\:of\:Cone}$

• $\sf{T.S.A\:of\:Cone}$

• $\sf{Volume\:of\:Cone}$

$\large{\underline{\purple{\rm{Formula\: used:}}}}$

• $\sf{C.S.A=\pi\:r\:l}$

• $\sf{T.S.A=\pi\:r(l+r)}$

• $\sf{Volume=\dfrac{1}{3}\pi\:r^2\:h}$

$\large{\underline{\orange{\rm{As\:per\: the\:above\: information:}}}}$

$\sf{\dashrightarrow l^2=r^2+h^2}$

$\sf{\dashrightarrow 50^2=14^2+h^2}$

$\sf{\dashrightarrow 2500=196+h^2}$

$\sf{\dashrightarrow h^2=2500-196}$

$\sf{\dashrightarrow h^2=2304}$

$\sf{\dashrightarrow h=\sqrt{2304}}$

$\sf\purple{\dashrightarrow h=48m}$

• Now finding the volume of cone

$\sf{\dashrightarrow Volume=\dfrac{1}{3}\pi\:r^2\:h}$

$\sf{\dashrightarrow Volume=\dfrac{1}{3}*\dfrac{22}{7}*14^2*48}$

$\sf{\dashrightarrow Volume=\dfrac{1*22*196*48}{3*7}}$

$\sf{\dashrightarrow Volume=\dfrac{\cancel{206976}}{\cancel{21}}}$

$\sf\purple{\dashrightarrow Volume=9856\:m^3}$

• Similarly, find the C.S.A of cone

$\sf{\dashrightarrow C.S.A=\pi\:r\:l}$

$\sf{\dashrightarrow C.S.A=\dfrac{22}{\cancel{7}}*\cancel{14}*50}$

$\sf{\dashrightarrow C.S.A=22*2*50}$

$\sf\purple{\dashrightarrow C.S.A=2200\:m^2}$

• Than, find the T.S.A of cone

$\sf{\dashrightarrow T.S.A=\pi\:r(l+r)}$

$\sf{\dashrightarrow T.S.A=\dfrac{22}{7}*14*(50+14)}$

$\sf{\dashrightarrow T.S.A=\dfrac{22}{\cancel{7}}*\cancel{14}*64}$

$\sf{\dashrightarrow T.S.A=22*2*64}$

$\sf\purple{\dashrightarrow T.S.A=2816\:m^2}$