Question

Find T.S.A and Volume of cone with radius 15 cm and height 20 cm ​

Answer 1

Answer:

Analysis→

Here we're given a cone whose radius is 15cm and height is 20cm. And we've to find the Total Surface Area(TSA) and Volume of the given.

And we know the volume of cone = $\rm{\dfrac{1}{3}πr^2h}$ and TSA of cone = $\rm{πr(r+l)}$.So let's divide the question into two parts. In the first part we've to find the tsa, and in the second part we've to find its volume. And taking $\rm{π=3.14}$

Given→

• Radius of cone = 15cm.
• Height of cone = 20cm.
• Assuming π = 3.14

To Find→

TSA and volume of the cone.

Answer→

$\Large{\underline{\underline{\mapsto{\rm{Total\:Surface\:Area}}}}}$

$\large{\underline{\boxed{\leadsto{\rm{TSA\:of\:Cone=πr(r+l)}}}}}$

$\rm\rightarrow{TSA=πr(r+l)}$

$\rm\rightarrow{TSA=3.14\times15cm(15cm+25)}$

$\rm\rightarrow{TSA=47.1cm(40cm)}$

$\rm\rightarrow{TSA=1884cm^2}$

${\boxed{\boxed{\rm{\rightarrow{TSA=1884cm^2✔}}}}}$

$\Large{\underline{\underline{\mapsto{\rm{Volume}}}}}$

$\large{\underline{\boxed{\leadsto{\rm{Volume\:of\:Cone=\dfrac{1}{3}πr^2h}}}}}$

$\rm\rightarrow{V=\dfrac{1}{3}πr^2h}$

$\rm\rightarrow{V=\dfrac{1}{3}\times3.14\times(15cm)^2(20cm)}$

$\rm\rightarrow{V=\dfrac{1}{\cancel{3}}\times3.14\times{\cancel{15cm}}\times15cm(20cm)}$

$\rm\rightarrow{V=3.14\times5cm\times15cm\times20cm}$

$\rm\rightarrow{V=15.7cm\times300cm^2}$

$\rm\rightarrow{V=4710cm^3}$

${\boxed{\boxed{\rightarrow{\rm{V=4710cm^3✔}}}}}$

☞ Hence the TSA of the cone is 1884cm² and the volume of the cone is 4710cm³ which is the required answer.

$\large{\underline{\boxed{\bigstar{NOTE\rightarrow}}}}$

Here we're not given the value of slant height(l), so we've to find its value. And we can find it by applying Pythagoras Theorem.

As l²=r²+h²

$\rm\rightarrow{l^2=r^2+h^2}$

$\rm\rightarrow{l^2=(15cm)^2+(20cm)^2}$

$\rm\rightarrow{l^2=225cm^2+400cm^2}$

$\rm\rightarrow{l^2=625cm^2}$

$\rm\rightarrow{l=\sqrt{625cm^2}}$

$\rm\rightarrow{l=25cm✔}$

HOPE IT HELPS.

$\Large\bf\color{steelblue}{@MissTranquillity}$