Question

in a right circular cone the
height is 3 times of the base. If its volume is 134.75 cm2 find area of base.​

Answer 1

Given:-

• Let the base radius of cone be r

• height is 3 times the radius of. base then height= 3r

• volume = 134.75cubic.cm

To find:-

The base area of cone

Now

According to your question:-

We know that

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

$\sf\implies \dfrac{1}{3}\pi r{}^{2} h=Volume\\ \\ \sf\implies \dfrac{1}{3}\times \dfrac{22}{7}\times r{}^{2}\times \cancel{3}r=134.75\\ \\ \sf\implies \dfrac{22}{7}\times r{}^{2}\times r=134.75\\ \\ \sf\implies r{}^{3}= \cancel{134.75}\times \dfrac{7}{\cancel{22}}\\ \\ \sf\implies r{}^{2}= 6.125\times 7\\ \\ \sf\implies r{}^{3}= 42.875\\ \\ \sf\implies r=</p><p>\sqrt[3]{42.875}\\ \\ \sf\implies r=\sqrt[3]{3.5\times 3.5\times 3.5}\\ \\ \sf\implies r=3.5cm$

• Now the radius of cone is 3.5cm

Height= 3×3.5 = 10.5cm

• Now we have to find the Area of base of cone

$\sf\underline{\bigstar{Area\:of\:base=\pi r{}^{2}}}$

$\sf\implies Area_{base}=\dfrac{22}{\cancel7}\times 3.5\times \cancel{3.5}\\ \\ \sf\implies Area\:of\:base= 22\times 3.5\times 0.5\\ \\ \sf\implies Area \:of\:base=38.5cm{}^{2}$

$\underline{\dag{\tt{Area\:of\:base=38.5cm{}^{2}}}}$

Answer 2

$\huge{\bf{\underline{\green{Answer :}}}}$

$\bold{\sf{\boxed{\black{Given :}}}}$

• Volume of Circular cone - $\bold{134.75 cm^{2}}$
• Height = 3r

$\bold{\boxed{\sf{To\ find :}}}$

• Area of Circular cone  base = ?

$\bold{\sf{\boxed{\purple{Solution :}}}}$

⇒Let the height of Circular cone - "h"

Let the radius of Circular cone  -  "r"

Now we find Radius through Volume of Circular Cone :

$\bold{Volume\ of \ circular\ cone} = \bold{\frac{1}{3}r^{2}h}$

$\implies \bold{\frac{1}{3}r^{2}h} = \bold{134.75 cm^{2} }$

∵ Given that : h = 3r

∴

$\implies \bold{\frac{1}{3}\ x\ \frac{22}{7}\ x \ r^{2}\ x\ 3r} = \bold{134.75 cm^{2}}$

$\implies \bold{r^{2} \ x \ 3r = \bold{\frac{134.75 \ x \ 3 \ x \ 7 }{22}}}$

$\implies \bold{r^{2} \ x \ 3r = 128.625 cm^{2}}$

$\implies \bold{r^{3} =\bold{ \frac{128.625}{3}}}$

$\implies \bold{r^{3} = \bold{42.875}}$

$\implies \bold{r = \bold{\sqrt[3]{42.875}}}$

$\implies \bold{r = \bold{\frac{42875}{1000}}}$

$\implies \bold{\underline{r = 3.5 cm }}$

Therefore ,

We have now radius so we find easily area of base :

$\implies \bold{Area \ of \ Circular \ cone \ Base} = \bold{\pi r^{2}}}$

$\implies \bold{\bold{\frac{22}{7} \ x \ 3.5 \ x \ 3.5 }}$

$\implies \bold{22 \ x \ 0.5 \ x \ 3.5}$

$\implies \bold{\boxed{38.5 \ cm^{2}}}$.........................Answer

If question in mention to  find height so :

h = 3r

h = 3 × 3.5

h = 10.5 cm