Question

find the slant height circular cone whose volume is 12936 CM.. and radius of the base is 21cm.also find its total surface area. ​

Answer 1

Solution :

Given, Volume of the cone

$V \: = 12936 cm^3$

Radius of the base of cone = 21 cm

We know that,

V = $\frac{1}{3} \pi {r}^{2} h$

So,

12936 = $\frac{1}{3} \pi {r}^{2} h \:$

$12936 \times \frac{7}{22} = \frac{1}{3} ( {21)}^{2} h \\ \\ 4116 \times 3 = 441h \\ \\ h = \frac{4116 \times 3}{441} = 28$

Also,

If slant height = l,

${l}^{2} = {r}^{2} + {h}^{2} \\ \\ \: \: = 21 ^{2} + ( {28}) ^{2} \\ \: \: = 441 + {784}\\ \: \: = 1225$

$l = \sqrt{1225} = 35$

$\boxed{ \textbf{ Slant height = 35 cm. }}$

_____________________________

Now, We are required to find TSA ( Total surface area)

TSA of cone = $\pi r(l+r)$

TSA = 22/7 ( 21) ( 21 + 35)

= 22 ( 3) ( 56)

= 3696 cm²

Answer 2

$\mathfrak{Step-by-step\:explanation:}$

$\underline{\underline{\bold{Given:}}}$

• Volume of the cone = 12936 cm³.
• Radius = 21 cm.

Let the height be h cm.

$\boxed{\bold{Volume\:of\:cone=\dfrac{1}{3}\pi r^2h.}}\\\\\\\implies\bold{\dfrac{1}{3}\pi r^2h=12936}\\\\\\\implies\bold{h=\dfrac{12936\times 3}{\pi \times 21 \times 21}}\\\\\\\implies\bold{h=\dfrac{88}{\pi}=88\times \dfrac{7}{22}}\\\\\\\implies\bold{h=4\times 7=28.}\\\\\\\boxed{\bold{Slant\:height(l)=\sqrt{h^2+r^2}}}\\\\\\\tt{=\sqrt{28^2+21^2}}\\\\\\\tt{=\sqrt{784+441}}\\\\\\\tt{=\sqrt{1225}=35\;cm.}\\\\\\\boxed{\boxed{\bold{Slant\:height=35\;cm.}}}$

$\boxed{\bold{Total\:Surface\:Area=\pi r(r+l).}}\\\\\\\tt{=\dfrac{22}{7}\times21(21+35)}\\\\\\\tt{=66\times 56=3696\:cm^2.}\\\\\\\boxed{\boxed{\bold{Total\:Surface\:Area=3696\:cm^2.}}}$