Question

A cone has base radius 5cm and height 24 cm .find CSA and TSA.​

Answer 1

Answer :

➥ Curved surface area of cone = 376.8 cm

➥ Total surface area of cone = 447.66 cm²

Given :

➤ Radius of the cone = 5 cm

➤ Height of the cone = 24 cm

To Find :

➤ Curved surface area of cone = ?

➤ Total surface area of cone = ?

Solution :

$\longmapsto \rm{Slant \: height \: cone \: (l) = \sqrt{ {h}^{2} + {b}^{2} } }$

$\longmapsto \rm{Slant \: height \: cone \: (l) = \sqrt{ {(24)}^{2} + {(5)}^{2} } }$

$\longmapsto \rm{Slant \: height \: cone \: (l) = \sqrt{576 + 25} }$

$\longmapsto \rm{Slant \: height \: cone \: (l) = \sqrt{601}}$

$\longmapsto \bf{Slant \: height \: cone \: (l) = 24.51}$

Now ,

Curved surface area of cone :

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

$\tt{: \implies C.S.A = \dfrac{22}{7} \times 5 \times 24}$

$\tt{: \implies C.S.A = 3.14 \times 5 \times 24}$

$\tt{: \implies C.S.A = 15.7 \times 24}$

$\tt{: \implies \green{ \underline{ \overline{ \boxed{ \purple{ \bf{ \: \: C.S.A = 376.8 \: cm \: \: }}}}}}}$

Hence, the curved surface area of cone is 376.8 cm.

Total surface area of cone :

$\tt{:\implies T.S.A = \pi rl + \pi r^2}$

$\tt{:\implies T.S.A = \pi r(r + 1)}$

$\tt{:\implies T.S.A = \dfrac{22}{7} \times 5(5 + 24.51)}$

$\tt{:\implies T.S.A = \dfrac{22}{7} \times 5 \times 29.51}$

$\tt{:\implies T.S.A = 3.14 \times 5 \times 29.51}$

$\tt{:\implies T.S.A = 15.17 \times 29.51}$

$\tt{:\implies \green{ \underline{ \overline{ \boxed{ \purple{ \bf{ \: \: T.S.A = 447.66 \: cm^2\: \: }}}}}} }$

Hence, the total surface area of cone is 447.66 cm².

Answer 2

Given :

• Radius of the cone = 5 cm

•  Height of the cone = 24 cm

To Find :

• Curved surface area of cone = ?

• Total surface area of cone = ?

We know :

• $\displaystyle We\:\:\:know \:\:Slant\:\:\:height \:\:of\:\:cone\:\:= \sqrt{h^{2}+b^{2}}$

• $=\displaystyle \sqrt{(24)^{2}+(5)^{2}}$

• $= \displaystyle \sqrt{(576)+(25)}}$

$\longrightarrow \displaystyle \sqrt{601} = 24.51$

Cone Curved surface area : π × r × l

                                               = $\frac{22}{7}$ cm × 5 cm  × 24 cm

                                               = 376.8 cm