Question

9. Find the volume, curved surface area and the total surface area of a cone whose height is 6 cm and slant height 10 cm. (Take pi = 3.14 )​

Answer 1

Given :-

Height of cone = 6 cm

Slant height = 10 cm

To Find :-

Volume

CSA

TSA

Solution :-

${\large{\boxed{\underline{\pmb{\sf{l^2=r^2+h^2}}}}}}$

$\rm\dashrightarrow (10)^2=r^2+(6)^2$

$\rm\dashrightarrow 100=r^2+36$

$\rm\dashrightarrow 100-36=r^2$

$\rm\dashrightarrow 64=r^2$

$\rm\dashrightarrow\sqrt{64}=r$

$\rm\dashrightarrow 8=r$

Now

We know that

${\large{\boxed{\underline{\pmb{\tt{Volume_{(Cone)}=\dfrac{1}{3}\pi r^2h}}}}}}$

$\rm\dashrightarrow Volume = \dfrac{1}{3}\times 3.14\times (8)^2\times6$

$\rm\dashrightarrow Volume=\dfrac{1}{3}\times 3.14\times 64\times6$

$\rm\dashrightarrow Volume=\dfrac{1}{\cancel{3}}\times 3.14\times 64\times\cancel{6}$

$\rm\dashrightarrow Volume=3.14\times64\times2$

$\rm\dashrightarrow Volume=401.92\;cm^3$

Now

${\large{\boxed{\underline{\pmb{\tt{CSA_{(Cone)}=\pi rl}}}}}}$

$\rm\dashrightarrow CSA=3.14\times8\times10$

$\rm\dashrightarrow CSA=3.14\times80$

$\rm\dashrightarrow CSA=251.2\;cm^2$

Now

${\large{\boxed{\underline{\pmb{\tt{TSA_{(Cone)}=\pi r(l+r)}}}}}}$

$\rm\dashrightarrow TSA=3.14\times 8(10+8)$

$\rm\dashrightarrow TSA=25.12\times18$

$\rm\dashrightarrow TSA=452.16 \;cm^2$

Therefore

Volume of cone is 401.92 cm³

CSA of cone is 251.2 cm² &

TSA of cone is 452.16 cm²

Answer 2

Find the volume, curved surface area and the total surface area of a cone whose height is 6 cm