Question

calculate the volume of a cone if the area of a base of right circular cone is 3850 sq m. and curve surface area is 4070 sq m.
options: (a) 14200 cube meter (b) 15500 cube meter (c) 15400 cube meter (d) 15000 cube meter. Give answer with explanation​

Answer 1

Given :

• Area of base of Right circular cone is 3850 m² .
• Curved Surface Area of Cone is 4070 m² .

To Find :

• Volume of Cone .

Solution :

Firstly we will find Radius :

Using Formula :

$\longmapsto\tt\boxed{Area\:of\:Circle=\pi{{r}^{2}}}$

Putting Values :

$\longmapsto\tt{3850=\dfrac{22}{7}\times{{r}^{2}}}$

$\longmapsto\tt{3850\times{7}=22\:{{r}^{2}}}$

$\longmapsto\tt{26950=22\:{{r}^{2}}}$

$\longmapsto\tt{\dfrac{26950}{22}={{r}^{2}}}$

$\longmapsto\tt{\sqrt{1225}=r}$

$\longmapsto\tt\bf{35\:m=r}$

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Now , We will calculate Slant Height :

Using Formula :

$\longmapsto\tt\boxed{C.S.A\:of\:Cone=\pi{rl}}$

Putting Values :

$\longmapsto\tt{4070=\dfrac{22}{{\cancel{7}}}\times{{\cancel{35}}}\times{l}}$

$\longmapsto\tt{4070=22\times{5}\times{l}}$

$\longmapsto\tt{4070=110\:l}$

$\longmapsto\tt{\cancel\dfrac{4070}{110}=l}$

$\longmapsto\tt\bf{37\:m=l}$

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For Height :

$\longmapsto\tt{{(l)}^{2}={(h)}^{2}+{(r)}^{2}}$

$\longmapsto\tt{{(37)}^{2}={(h)}^{2}+{(35)}^{2}}$

$\longmapsto\tt{1369={(h)}^{2}+1225}$

$\longmapsto\tt{1369-1225={(h)}^{2}}$

$\longmapsto\tt{\sqrt{144}=h}$

$\longmapsto\tt\bf{12\:m=h}$

Now ,

For Volume :

Using Formula :

$\longmapsto\tt\boxed{Volume\:of\:Cone=\dfrac{1}{3}\pi{{r}^{2}h}}$

Putting Values :

$\longmapsto\tt{\dfrac{1}{{\cancel{3}}}\times\dfrac{22}{{\cancel{7}}}\times{{\cancel{35}}}\times{35}\times{{\cancel{12}}}}$

$\longmapsto\tt{22\times{35}\times{20}}$

$\longmapsto\tt\bf{15400\:{m}^{3}}$

So , The Volume of Cone is 15400 m³ .

Option c ) 15400 m³ is Correct .

Answer 2

To Find:-

• Find the volume of the cone.

Given:-

• Area of a base of right circular cone is 3850m².
• Curve surface area is 4070m²

Solution:-

We know that:-

$\tt\implies \: Area \: of \: circle \: = \pi{r}^{2}$

$\tt\implies \: 3850 = \dfrac{22}{7} \times {r}^{2}$

$\tt\implies \: {r}^{2} = \dfrac{3850 \times 7 }{22}$

$\tt\implies \: r = \sqrt{1225}$

$\tt\implies \: r = 35m$

Now,

$\tt\implies \: C.S.A = \pi rl$

Substituting Values:-

$\tt\implies \: 4070 = \dfrac{22}{7} \times 35 \times l$

$\tt\implies \: 4070 = 110 l$

$\tt\implies \: l = \cancel\dfrac{4070}{110}$

$\tt\implies \: l = 37m$

To Find height:-

$\tt\implies \: {l}^{2} = {h}^{2} + {r}^{2}$

$\tt\implies \: {(37)}^{2} = {h}^{2} + {(35)}^{2}$

$\tt\implies \: 1369 = {h}^{2} + 1225$

$\tt\implies \: {h}^{2} = 1369 - 1225$

$\tt\implies \: h = \sqrt{144}$

$\tt\implies \: h = 12m$

Now,

To Find the volume of cone

$\tt\implies \: Volume \: \: of \: \: Cone = \dfrac{1}{3} \pi {r}^{2} h$

$\tt\implies \: \dfrac{1}{3} \times \dfrac{22}{7} \times 35 \times 35 \times 12$

$\tt\implies \: {15400m}^{3}$