Question

volume of the cone is 1232, r=7 find total surface area ​

Answer 1

Step-by-step explanation:

hope it helps

s mark brainliest

Answer 2

$\large \pink{\underline{\boxed{ \rm{}Required\:Answer}}}$

Diagram:

$\setlength{\unitlength}{1.2mm}\begin{picture}(5,5)\thicklines\put(0,0){\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\put(-0.5,-1){\line(1,2){13}}\put(25.5,-1){\line(-1,2){13}}\multiput(12.5,-1)(2,0){7}{\line(1,0){1}}\multiput(12.5,-1)(0,4){7}{\line(0,1){2}}\put(18,1.6){\sf{7(radius)}}\put(9.5,10){\sf{? (Height)}}\end{picture}$

If you can't see the diagram then take a look on attached picture

Given:

• Volume of Cone = 1232

• radius = 7

To find :

• Area

We know:

Formula of cone:-

$\bigstar\boxed{ \rm{}Area \: of \: Cone =\pi \: r(r + \sqrt{ {h}^{2} + {r}^{2} } )}$

So as we can see to find area of cone we need height of cylinder.

So first let's find height of cone:

We can find by using formula volume of cone:

$\bigstar \boxed{ \rm{}Volume \: of \: Cone = \pi {r}^{2} \times \frac{h}{3} }$

So let's find it!

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

$\dashrightarrow \sf 1232= \dfrac{22}{7} \times {7}^{2} \times \dfrac{h}{3}$

$\dashrightarrow \sf 1232= \dfrac{22}{7} \times7 \times 7\times \dfrac{h}{3}$

$\dashrightarrow \sf 1232= \dfrac{22}{\cancel7} \times\cancel7 \times 7\times \dfrac{h}{3}$

$\dashrightarrow \sf 1232= \dfrac{22}{1}\times 7\times \dfrac{h}{3}$

$\dashrightarrow \sf 1232= \dfrac{22 \times 7 \times h}{3}$

$\dashrightarrow \sf 1232 \times \dfrac{3}{22 \times 7} =h$

$\dashrightarrow \sf \cancel{1232} \times \dfrac{3}{\cancel{22 }\times 7} =h$

$\dashrightarrow \sf 56 \times \dfrac{3}{ 7} =h$

$\dashrightarrow \sf \cancel{56} \times \dfrac{3}{\cancel{ 7}} =h$

$\dashrightarrow \sf h = 3 \times 8$

$\dashrightarrow\underline{\boxed {\sf h = 24}}$

Now Let's find area by using the formula which is mentioned first:

$\dashrightarrow\sf{}Area \: of \: Cone =\pi \: r(r + \sqrt{ {h}^{2} + {r}^{2} } )$

$\dashrightarrow\sf{}Area \: of \: Cone = \dfrac{22}{7} \: \times 7(7+ \sqrt{ {(24)}^{2} + {(7)}^{2} } )$

$\dashrightarrow\sf{}Area \: of \: Cone = \dfrac{22}{7} \: \times 7(7+ \sqrt{ 576 + {49}} )$

$\dashrightarrow\sf{}Area \: of \: Cone = \dfrac{22}{7} \: \times 7(7+ \sqrt{ 625} )$

$\dashrightarrow\sf{}Area \: of \: Cone = \dfrac{22}{7} \: \times 7(7+ \sqrt{ 5 \times 5 \times 5 \times 5} )$

$\dashrightarrow\sf{}Area \: of \: Cone = \dfrac{22}{7} \: \times 7(7+ \sqrt{ {5}^{2} \times {5}^{2} } )$

$\dashrightarrow\sf{}Area \: of \: Cone = \dfrac{22}{7} \: \times 7(7+ 5 \times 5)$

$\dashrightarrow\sf{}Area \: of \: Cone = \dfrac{22}{7} \: \times 7(7+25)$

$\dashrightarrow\sf{}Area \: of \: Cone = \dfrac{22}{\cancel7} \: \times \cancel7(7+25)$

$\dashrightarrow\sf{}Area \: of \: Cone = 22 \times (7 + 25)$

$\dashrightarrow\sf{}Area \: of \: Cone = 22 \times 32$

$\dashrightarrow \underline{\boxed{\sf{}Area \: of \: Cone = 704}}$

Note:-

as no units are mentioned.°. final answer also have no units

Happy learning! :)